Finite Group Databasebeta

← #29601726

Subgroups — #29601726

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519734C211yesmaximal, characteristic
2C2×C4×#11758196C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic
5C2×C4×#11758198C211yesmaximal, characteristic
6#21444083C212yesmaximal, complemented
7#21444074C212yesmaximal, complemented
8#21444065C212yesmaximal
9#21444063C212yesmaximal
10C4×#14519684C211yesmaximal, characteristic, complemented
11C4×#95×C61C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C2×#14519734—24no—
14C2×#14519734—24no—
15C2×#14519734—24no—
16C22×C4⋊Dic61C2212yes—
17C22×#11758196C2212yes—
18C22×#11758196C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C4×#11758196—24no—
27C4×C4⋊Dic61—24no—
28C4×#11758198—24no—
29C4×#11758198C418yescomplemented
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C22×C42×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2212yes—
42C24×D61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2312yes—
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C23×Dic61C2311yescharacteristic
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61C2×C414yes—
53C22×C4×D61D414yes—
54C22×C4×D61Q814yes—
55#14519734—232no—
56C2×C4⋊Dic61—24no—
57C2×C4⋊Dic61—24no—
58C2×C4⋊Dic61—24no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758196—24no—
63C2×#11758196—24no—
64C2×#11758196—24no—
65C2×#11758198—24no—
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198C2×C414yes—
74C2×#11758198C2×C414yes—
75C2×C4×Dic61—22no—
76C2×C4×Dic61—22no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61—22no—
79C2×C4×Dic61—22no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—22no—
82C2×C4×Dic61C2×C414yes—
83C2×C4×Dic61D414yes—
84#14519684—24no—
85#14519684—24no—
86#14519684—24no—
87#14519684—24no—
88#14519684—24no—
89#14519684C2×C414yes—
90#14519684C2×C414yes—
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2312yes—
93C23×C4×C61C2312yes—
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2311yescharacteristic
96C2×C42×C61—22no—
97C2×C42×C61—22no—
98C2×C42×C61—22no—
99C2×C42×C61—22no—
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102C2×C42×C61—22no—
103C2×C42×C61C2×C414yes—
104C2×C42×C61D414yes—
105#95×C61—24no—
106#95×C61—24no—
107C24×C61C2411yescharacteristic
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61C22×C412yes—
117C23×D61C2×D412yes—
118C23×D61C2×Q812yes—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61C22×C412yes—
139C22×C4×C61C22×C412yes—
140C22×C4×C61C22×C412yes—
141C22×C4×C61C2×D414yes—
142C22×C4×C61C2×D412yes—
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D412yes—
145C22×C4×C61C2×Q812yes—
146C22×C4×C61#4114yes—
147C22×C4×C61#4114yes—
148C22×C4×C61#4112yes—
149C22×C4×C61#4112yes—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61C22×C412yes—
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C412yes—
176C22×Dic61C2×D414yes—
177C22×Dic61C2×D412yes—
178C22×Dic61C2×Q812yes—
179C22×Dic61#4114yes—
180C22×Dic61#4114yes—
181C2×C4×D61—28no—
182C2×C4×D61—28no—
183C2×C4×D61—28no—
184C2×C4×D61—28no—
185C2×C4×D61—28no—
186C2×C4×D61—28no—
187C2×C4×D61C4⋊C4116yescomplemented
188C42×C61—28no—
189C42×C61—28no—
190C42×C61—44no—
191#11758198—216no—
192#11758198—216no—
193#11758198—28no—
194#11758198—28no—
195C4⋊Dic61—216no—
196#11758196—216no—
197#11758196—216no—
198C4×Dic61—28no—
199C4×Dic61—28no—
200C4×Dic61—44no—
201C23×C61C23×C411yescharacteristic
202C23×C61C22×D411yescharacteristic
203C23×C61C22×D411yescharacteristic
204C23×C61C22×D411yescharacteristic
205C23×C61C22×Q811yescharacteristic
206C23×C61C2×#4112yes—
207C23×C61C2×#4112yes—
208C23×C61C2×#4111yescharacteristic
209C23×C61C2×#4111yescharacteristic
210C23×C61C2×#4112yes—
211C23×C61C2×#4112yes—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—24no—
223C22×D61—24no—
224C22×D61—24no—
225C22×D61—24no—
226C22×D61—42no—
227C22×D61—42no—
228C22×D61—42no—
229C22×D61—42no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61—42no—
234C22×D61C2×C4⋊C414yes—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—24no—
246C2×C4×C61—24no—
247C2×C4×C61—24no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61C2×C4⋊C414yes—
259C2×C4×C61#11714yescomplemented
260C2×C4×C61C4×D414yes—
261C2×C4×C61C4×D414yes—
262C2×C4×C61#12014yes—
263C2×C4×C61C22⋊Q814yes—
264C2×C4×C61C22⋊Q814yes—
265C2×C4×C61#12314yes—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—24no—
275C2×Dic61—24no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—24no—
282C2×Dic61—24no—
283C2×Dic61—24no—
284C2×Dic61—24no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61C2×C4⋊C414yes—
296C2×Dic61#11714yescomplemented
297C4×D61—232no—
298#13844—611nomaximal, Sylow
299C22×C61C22×C4⋊C411yescharacteristic
300C22×C61C2×#11711yescharacteristic
301C22×C61C2×#11711yescharacteristic
302C22×C61C2×C4×D411yescharacteristic
303C22×C61C2×C4×D411yescharacteristic
304C22×C61C4×#4111yescharacteristic
305C22×C61C4×#4111yescharacteristic
306C22×C61C2×#12011yescharacteristic
307C22×C61C2×C22⋊Q811yescharacteristic
308C22×C61C2×C22⋊Q811yescharacteristic
309C22×C61C2×#12311yescharacteristic
310C22×C61#52512yes—
311C22×C61#52512yes—
312C22×C61#52512yes—
313C22×C61#52912yes—
314C22×C61#52912yes—
315C22×C61#52912yes—
316C22×C61#52912yes—
317C22×C61#53212yes—
318C22×C61#53212yes—
319C22×C61#53212yes—
320C22×C61#53312yes—
321C22×C61#53312yes—
322C2×D61—24no—
323C2×D61—24no—
324C2×D61—24no—
325C2×D61—44no—
326C2×D61—44no—
327C2×D61—44no—
328C2×D61—44no—
329C2×D61—42no—
330C2×D61—42no—
331C2×D61—42no—
332C2×D61—42no—
333C4×C61—24no—
334C4×C61—44no—
335C4×C61—44no—
336C4×C61—42no—
337C4×C61#38518yes—
338Dic61—24no—
339Dic61—24no—
340Dic61—44no—
341Dic61—44no—
342Dic61—42no—
343C22×#117—611no—
344C2×C4×C4⋊C4—611no—
345C2×C4×C4⋊C4—611no—
346C2×C4×C22⋊C4—611no—
347C2×C4×C22⋊C4—611no—
348#1444—612no—
349#1442—612no—
350#1439—612no—
351#1439—612no—
352C4×#95—611no—
353C4×#95D6111yescharacteristic, complemented
354C2×C61#228511yescharacteristic
355C2×C61C2×#38511yescharacteristic
356C2×C61#229011yescharacteristic
357C2×C61#229011yescharacteristic
358C2×C61#229311yescharacteristic
359C2×C61#229311yescharacteristic
360C2×C61#229611yescharacteristic
361C2×C61#238812yes—
362C2×C61#239512yes—
363C2×C61#239612yes—
364C2×C61#239612yes—
365D61—44no—
366C24×C4—611no—
367C2×#117—1224no—
368C2×#117—1224no—
369C2×#117—1224no—
370C22×C4⋊C4—612no—
371C22×C4⋊C4—612no—
372C22×C4⋊C4—612no—
373C22×C22⋊C4—611no—
374C22×C22⋊C4—611no—
375C22×C22⋊C4—612no—
376C22×C22⋊C4—612no—
377C22×C42—611no—
378C22×C42—611no—
379C22×C42—611no—
380C22×C42C2×D6111yescharacteristic
381C22×C42C2×D6111yescharacteristic
382C22×C42C2×D6111yescharacteristic
383C4×C4⋊C4—1224no—
384C4×C4⋊C4—1224no—
385C4×C22⋊C4—618no—
386C4×C22⋊C4—1224no—
387C2×#95—611no—
388C2×#95—611no—
389C2×#95—612no—
390C2×#95—612no—
391C2×#95—612no—
392C2×#95—612no—
393C2×#95—612no—
394C2×#95C2×D6112yes—
395C2×#95C2×D6112yes—
396C61#1384411yescharacteristic, complemented, Sylow
397C25—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—614no—
401C23×C4—614no—
402C23×C4—614no—
403C23×C4—612no—
404C23×C4—612no—
405C23×C4—611no—
406C23×C4—1222no—
407C23×C4—1222no—
408C23×C4—1222no—
409C23×C4—1222no—
410C23×C4C22×D6111yescharacteristic
411C23×C4C22×D6112yes—
412C23×C4C22×D6112yes—
413C23×C4C22×D6111yescharacteristic
414C23×C4C22×D6111yescharacteristic
415#117—12232no—
416C2×C4⋊C4—1224no—
417C2×C4⋊C4—1224no—
418C2×C4⋊C4—1224no—
419C2×C4⋊C4—1224no—
420C2×C4⋊C4—1224no—
421C2×C4⋊C4—1224no—
422C2×C4⋊C4—1224no—
423C2×C4⋊C4—1224no—
424C2×C4⋊C4—1224no—
425C2×C22⋊C4—614no—
426C2×C22⋊C4—614no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4—1224no—
429C2×C22⋊C4—1224no—
430C2×C22⋊C4—1224no—
431C2×C22⋊C4—1224no—
432C2×C22⋊C4—1224no—
433C2×C22⋊C4—1224no—
434C2×C22⋊C4—1224no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—614no—
443C2×C42—614no—
444C2×C42—1222no—
445C2×C42—1222no—
446C2×C42—1222no—
447C2×C42—1222no—
448C2×C42—1222no—
449C2×C42—1222no—
450C2×C42—1222no—
451C2×C42C4×D6114yes—
452C2×C42D24414yes—
453#95—24no—
454#95—24no—
455#95—614no—
456#95—614no—
457#95—1224no—
458#95—1224no—
459#95—1224no—
460#95—1224no—
461#95—1224no—
462C24—612no—
463C24—612no—
464C24—612no—
465C24—1221no—
466C24—1221no—
467C24—1222no—
468C24—1222no—
469C24—1221no—
470C24—1222no—
471C24—1222no—
472C24—1221no—
473C24C23×D6111yescharacteristic
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—612no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—612no—
497C22×C4—614no—
498C22×C4—6116no—
499C22×C4—612no—
500C22×C4—614no—
501C22×C4—614no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1222no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1228no—
510C22×C4—1228no—
511C22×C4—1228no—
512C22×C4—1228no—
513C22×C4—1228no—
514C22×C4—1228no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—1222no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—1221no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4C2×C4×D6112yes—
532C22×C4C2×C4×D6112yes—
533C22×C4C2×C4×D6112yes—
534C22×C4C2×D24414yes—
535C22×C4C2×D24412yes—
536C22×C4#1175822214yes—
537C22×C4#1175822214yes—
538C22×C4#1175822212yes—
539C22×C4D4×D6112yes—
540C22×C4D4×D6112yes—
541C22×C4#1175822412yes—
542C22×C4Q8×D6112yes—
543C4⋊C4—12216no—
544C4⋊C4—12216no—
545C4⋊C4—12216no—
546C22⋊C4—1228no—
547C22⋊C4—12216no—
548C22⋊C4—12216no—
549C22⋊C4—1228no—
550C42—28no—
551C42—28no—
552C42—44no—
553C42—1228no—
554C42—1228no—
555C42—2444no—
556C23—614no—
557C23—1222no—
558C23—1222no—
559C23—1222no—
560C23—1222no—
561C23—1222no—
562C23—1222no—
563C23—1222no—
564C23—1222no—
565C23—1222no—
566C23—1222no—
567C23—1224no—
568C23—1224no—
569C23—1224no—
570C23—1224no—
571C23—2442no—
572C23—2442no—
573C23—2442no—
574C23—2442no—
575C23—2442no—
576C23—2442no—
577C23—2442no—
578C23—2442no—
579C23C22×C4×D6111yescharacteristic
580C23C2×D4×D6111yescharacteristic
581C23C2×D4×D6111yescharacteristic
582C23C22×D24411yescharacteristic
583C23C2×Q8×D6111yescharacteristic
584C23#41×D6112yes—
585C23#41×D6112yes—
586C23C2×#1175822411yescharacteristic
587C23C2×#1175822212yes—
588C23C2×#1175822211yescharacteristic
589C23C2×#1175822212yes—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—614no—
614C2×C4—614no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1224no—
624C2×C4—1224no—
625C2×C4—12232no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1224no—
630C2×C4—1224no—
631C2×C4—1224no—
632C2×C4—1224no—
633C2×C4—1224no—
634C2×C4—1224no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2442no—
638C2×C4—2442no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4—2442no—
642C2×C4—2442no—
643C2×C4—2442no—
644C2×C4—2442no—
645C2×C4C4⋊C4×D6114yes—
646C2×C4#1451973414yescomplemented
647C2×C4#1451973714yes—
648C2×C4C4×D24414yes—
649C2×C4#1451974714yes—
650C2×C4#1451975514yes—
651C2×C4#1451975714yes—
652C2×C4#1451975914yes—
653C22—1224no—
654C22—1224no—
655C22—1224no—
656C22—2442no—
657C22—2442no—
658C22—2444no—
659C22—2442no—
660C22—2442no—
661C22—2444no—
662C22—2444no—
663C22—2444no—
664C22C2×C4⋊C4×D6111yescharacteristic
665C22#117×D6111yescharacteristic
666C22C2×#1451973411yescharacteristic
667C22C2×#1451973711yescharacteristic
668C22C2×C4×D24411yescharacteristic
669C22#1684023011yescharacteristic
670C22C4×#1175822211yescharacteristic
671C22C2×#1451974711yescharacteristic
672C22C2×#1451975511yescharacteristic
673C22C2×#1451975711yescharacteristic
674C22C2×#1451975911yescharacteristic
675C22#1684027112yes—
676C22#1684027112yes—
677C22#1684027412yes—
678C22#1684029012yes—
679C22#1684029212yes—
680C22#1684029212yes—
681C22#1684029612yes—
682C22#1684030912yes—
683C22#1684030912yes—
684C22#1684031212yes—
685C22#1684031612yes—
686C22#1684031612yes—
687C4—24no—
688C4—44no—
689C4—42no—
690C4—44no—
691C4—1224no—
692C4—1224no—
693C4—2444no—
694C4—2444no—
695C4—2442no—
696C4#1683963618yes—
697C2—2444no—
698C2#2144822311yescharacteristic
699C2C2×#1683963611yescharacteristic
700C2#2144825811yescharacteristic
701C2#2144826311yescharacteristic
702C2#2144828211yescharacteristic
703C2#2144828311yescharacteristic
704C2#2144829911yescharacteristic
705C2#2144903512yes—
706C2#2144908012yes—
707C2#2144909112yes—
708C2#2144909512yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4×#95D61
hypocenterC61#13844
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×#11758196C2semidirect
3. C2×C4×C4⋊Dic61C2semidirect
6. #21444083C2semidirect
7. #21444074C2semidirect
10. C4×#14519684C2semidirect
11. C4×#95×C61C2semidirect
29. C4×#11758198C4semidirect
187. C2×C4×D61C4⋊C4semidirect
259. C2×C4×C61#117semidirect
296. C2×Dic61#117semidirect
353. C4×#95D61semidirect
396. C61#13844semidirect
646. C2×C4#14519734semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145197342
C2×C4×#117581962
C2×C4×C4⋊Dic612
C2×C4×#117581982
#214440832
#214440742
#214440652
#214440632
C4×#145196842
C4×#95×C612
#1384461