Finite Group Databasebeta

← C3×#23427 #10642034

Subgroups — C3×#23427 #10642034

Order 768.

1986 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2C22×C3×#135C211yesmaximal, characteristic
3C2×C3×#536C211yesmaximal, characteristic, complemented
4C2×C3×#417C211yesmaximal, characteristic, complemented
5C22×C3×#103C211yesmaximal, characteristic, complemented
6C3×#2311C211yesmaximal, characteristic, complemented
7C3×#2016C212yesmaximal, complemented
8C3×#2015C212yesmaximal, complemented
9C3×#2013C212yesmaximal, complemented
10C3×#2012C212yesmaximal, complemented
11C3×#1729C211yesmaximal, characteristic, complemented
12#23427C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C22×C3×#41C2211yescharacteristic
15C23×C3×Q8C2211yescharacteristic
16C2×C3×#137—24no—
17C2×C3×#137—24no—
18C2×C3×#137—24no—
19C2×C3×#135—24no—
20C2×C3×#135—24no—
21C2×C3×#135—24no—
22C22×C3×Q16C2212yes—
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2212yes—
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29C23×C3×C8C2211yescharacteristic
30C3×#536—24no—
31C3×#536—24no—
32C2×C3×C4⋊Q8C2212yes—
33C2×C3×#124C2212yes—
34C2×C3×#123—22no—
35C2×C3×C22⋊Q8—22no—
36C2×C3×#117C2211yescharacteristic
37C22×C3×C4⋊C4C2211yescharacteristic
38C3×#417—24no—
39C2×C3×#103—24no—
40C2×C3×#103C2212yes—
41C2×C3×#103C2212yes—
42C2×C3×#103C2212yes—
43C2×C3×#102C2212yes—
44C3×#391C2212yes—
45C3×#390C2212yes—
46C3×#386—22no—
47C3×#380—22no—
48C3×#336C2212yes—
49C3×#336C2212yes—
50C22×#137C2×C311yescharacteristic, complemented
51C22×#135C2×C311yescharacteristic
52C2×#536C2×C311yescharacteristic, complemented
53C2×#417C2×C311yescharacteristic, complemented
54C22×#103C2×C311yescharacteristic, complemented
55#2311C2×C311yescharacteristic, complemented
56#2016C2×C312yescomplemented
57#2015C2×C312yescomplemented
58#2013C2×C312yescomplemented
59#2012C2×C312yescomplemented
60#1729C2×C311yescharacteristic, complemented
61C2×C3×#41—22no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41—22no—
68C2×C3×#41—22no—
69C2×C3×#41—22no—
70C2×C3×#41—22no—
71C2×C3×#41D414yes—
72C2×C3×#41D414yes—
73C22×C3×Q8—21no—
74C22×C3×Q8—22no—
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8D414yes—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2312yes—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4C2311yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C3×#137—232no—
93C3×#135—232no—
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—24no—
97C2×C3×Q16—24no—
98C2×C3×Q16—22no—
99C2×C3×Q16—24no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—24no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—24no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—24no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C2×C3×D8—22no—
112C2×C3×M16—22no—
113C2×C3×M16—22no—
114C2×C3×M16D414yes—
115C22×C3×C8—22no—
116C22×C3×C8—22no—
117C22×C3×C8D414yes—
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2312yes—
121C3×C4⋊Q8—24no—
122C3×C4⋊Q8—24no—
123C3×#124—24no—
124C3×#124—24no—
125C3×#123—216no—
126C3×C22⋊Q8—216no—
127C3×#117—22no—
128C3×#117—22no—
129C2×C3×C4⋊C4—24no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4D412yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4D412yes—
138C2×C3×C42C2312yes—
139C3×#103—24no—
140C3×#103—24no—
141C3×#103—24no—
142C3×#102—24no—
143C3×#95—24no—
144C22×#41C22×C311yescharacteristic
145C22×#41C22×C311yescharacteristic
146C23×Q8C22×C311yescharacteristic
147C2×#137—24no—
148C2×#137—24no—
149C2×#137—24no—
150C2×#135—24no—
151C2×#135—24no—
152C2×#135—24no—
153C22×Q16C22×C312yes—
154C22×Q16C22×C311yescharacteristic
155C22×SD16C22×C312yes—
156C22×SD16C22×C311yescharacteristic
157C22×SD16C22×C311yescharacteristic
158C22×D8C22×C311yescharacteristic
159C22×M16C22×C311yescharacteristic
160C23×C8C22×C311yescharacteristic
161#536—24no—
162#536—24no—
163C2×C4⋊Q8C22×C312yes—
164C2×#124C22×C312yes—
165C2×#123—22no—
166C2×C22⋊Q8—22no—
167C2×#117C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic
169#417—24no—
170C2×#103—24no—
171C2×#103C22×C312yes—
172C2×#103C22×C312yes—
173C2×#103C22×C312yes—
174C2×#102C22×C312yes—
175#391C22×C312yes—
176#390C22×C312yes—
177#386—22no—
178#380—22no—
179#336C22×C312yes—
180#336C22×C312yes—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3C2×D411yescharacteristic
184C3×#41—28no—
185C3×#41—28no—
186C3×#41—28no—
187C3×#41—28no—
188C3×#41—44no—
189C3×#41—44no—
190C3×#41—44no—
191C3×#41—44no—
192C2×C3×Q8—24no—
193C2×C3×Q8—22no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—28no—
197C2×C3×Q8—28no—
198C2×C3×Q8—22no—
199C2×C3×Q8—21no—
200C2×C3×Q8—22no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—22no—
209C2×C3×Q8—21no—
210C2×C3×Q8—44no—
211C2×C3×Q8—42no—
212C2×C3×Q8—44no—
213C2×C3×Q8—42no—
214C2×C3×Q8C2×D414yes—
215C2×C3×Q8C2×D412yes—
216C2×C3×Q8C2×D412yes—
217C2×C3×D4—24no—
218C2×C3×D4—24no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4C2×D412yes—
234C2×C3×D4C2×D412yes—
235C22×C3×C4—24no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—22no—
242C22×C3×C4—42no—
243C22×C3×C4—42no—
244C22×C3×C4—42no—
245C22×C3×C4—42no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4—82no—
250C22×C3×C4C2×D414yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D412yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4#4112yes—
258C22×C3×C4C2411yescharacteristic
259C3×Q16—28no—
260C3×Q16—216no—
261C3×SD16—28no—
262C3×SD16—28no—
263C3×SD16—216no—
264C3×D8—28no—
265C3×M16—28no—
266C2×C3×C8—28no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C2×C3×C8C2×D414yes—
274C2×C3×C8C2×D412yes—
275C2×C3×C8C2×D412yes—
276C3×C4⋊C4—216no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—42no—
281C3×C22⋊C4—216no—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—84no—
284C3×C42—22no—
285C3×C42—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41C3×D414yes—
297C2×#41C3×D414yes—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8C3×D414yes—
305C22×Q8C23×C312yes—
306C22×Q8C23×C311yescharacteristic
307C22×Q8C23×C311yescharacteristic
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C23×C311yescharacteristic
311C22×D4C23×C311yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4C23×C311yescharacteristic
317#137—232no—
318#135—232no—
319C2×Q16—22no—
320C2×Q16—22no—
321C2×Q16—24no—
322C2×Q16—24no—
323C2×Q16—22no—
324C2×Q16—24no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—24no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—24no—
331C2×SD16—22no—
332C2×SD16—22no—
333C2×SD16—24no—
334C2×D8—22no—
335C2×D8—22no—
336C2×D8—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16C3×D414yes—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8C3×D414yes—
343C22×C8C23×C311yescharacteristic
344C22×C8C23×C311yescharacteristic
345C22×C8C23×C312yes—
346C4⋊Q8—24no—
347C4⋊Q8—24no—
348#124—24no—
349#124—24no—
350#123—216no—
351C22⋊Q8—216no—
352#117—22no—
353#117—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C3×D412yes—
359C2×C4⋊C4C23×C312yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4C3×D412yes—
363C2×C42C23×C312yes—
364#103—24no—
365#103—24no—
366#103—24no—
367#102—24no—
368#95—24no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3#12012yes—
382C23×C3#12112yes—
383C23×C3#12712yes—
384C23×C3C22×D411yescharacteristic
385C3×Q8—24no—
386C3×Q8—22no—
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—24no—
390C3×Q8—22no—
391C3×Q8—42no—
392C3×Q8—41no—
393C3×Q8—42no—
394C3×Q8—41no—
395C3×Q8—41no—
396C3×Q8—41no—
397C3×Q8—48no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—48no—
403C3×D4—48no—
404C3×D4—41no—
405C3×D4—41no—
406C3×D4—41no—
407C3×D4—41no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—42no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—42no—
420C2×C3×C4—48no—
421C2×C3×C4—48no—
422C2×C3×C4—48no—
423C2×C3×C4—42no—
424C2×C3×C4—44no—
425C2×C3×C4—84no—
426C2×C3×C4#12014yes—
427C2×C3×C4#12014yes—
428C2×C3×C4#12012yes—
429C2×C3×C4#12114yes—
430C2×C3×C4#12114yes—
431C2×C3×C4#12112yes—
432C2×C3×C4#12712yes—
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C22×D411yescharacteristic
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C3×C8—22no—
440C3×C8—22no—
441C3×C8—24no—
442C24—21no—
443C24—21no—
444C24C2×C3×D411yescharacteristic
445#41—28no—
446#41—28no—
447#41—28no—
448#41—28no—
449#41—44no—
450#41—44no—
451#41—44no—
452#41—44no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—21no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8C2×C3×D414yes—
476C2×Q8C2×C3×D412yes—
477C2×Q8C2×C3×D412yes—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4C2×C3×D412yes—
495C2×D4C2×C3×D412yes—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—82no—
511C22×C4C2×C3×D414yes—
512C22×C4C2×C3×D412yes—
513C22×C4C2×C3×D412yes—
514C22×C4C2×C3×D412yes—
515C22×C4C2×C3×D411yescharacteristic
516C22×C4C2×C3×D412yes—
517C22×C4C2×C3×D412yes—
518C22×C4C3×#4112yes—
519C22×C4C24×C311yescharacteristic
520Q16—28no—
521Q16—216no—
522SD16—28no—
523SD16—28no—
524SD16—216no—
525D8—28no—
526M16—28no—
527C2×C8—28no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8C2×C3×D414yes—
535C2×C8C2×C3×D412yes—
536C2×C8C2×C3×D412yes—
537C4⋊C4—216no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—42no—
542C22⋊C4—216no—
543C22⋊C4—24no—
544C22⋊C4—84no—
545C42—22no—
546C42—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—81no—
556C22×C3—81no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3—82no—
560C22×C3—82no—
561C22×C3#39214yes—
562C22×C3C2×#12011yescharacteristic
563C22×C3C2×#12111yescharacteristic
564C22×C3C2×#12711yescharacteristic
565C22×C3#57712yes—
566C22×C3#57812yes—
567C3×C4—42no—
568C3×C4—42no—
569C3×C4—44no—
570C3×C4—44no—
571C3×C4—82no—
572C3×C4#39214yes—
573C3×C4C2×#12011yescharacteristic
574C3×C4C2×#12011yescharacteristic
575C3×C4C2×#12111yescharacteristic
576C3×C4C2×#12111yescharacteristic
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C3×#12012yes—
590C23C3×#12112yes—
591C23C3×#12712yes—
592C23C22×C3×D411yescharacteristic
593Q8—24no—
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—24no—
598Q8—22no—
599Q8—48no—
600Q8—42no—
601Q8—41no—
602Q8—42no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606D4—22no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—48no—
611D4—48no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—48no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—48no—
630C2×C4—48no—
631C2×C4—44no—
632C2×C4—42no—
633C2×C4—84no—
634C2×C4C3×#12012yes—
635C2×C4C3×#12014yes—
636C2×C4C3×#12014yes—
637C2×C4C3×#12112yes—
638C2×C4C3×#12114yes—
639C2×C4C3×#12114yes—
640C2×C4C3×#12712yes—
641C2×C4C22×C3×D411yescharacteristic
642C2×C4C22×C3×D411yescharacteristic
643C2×C4C22×C3×D411yescharacteristic
644C2×C4C22×C3×D411yescharacteristic
645C2×C4C22×C3×D411yescharacteristic
646C2×C4C2×C3×#4111yescharacteristic
647C8—22no—
648C8—22no—
649C8—24no—
650C2×C3—24no—
651C2×C3—82no—
652C2×C3—82no—
653C2×C3C2×#39211yescharacteristic
654C2×C3#301312yes—
655C2×C3#304612yes—
656C2×C3#315411yescharacteristic
657C2×C3#315611yescharacteristic
658C22—22no—
659C22—22no—
660C22—24no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—44no—
665C22—44no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—82no—
671C22—82no—
672C22C3×#39214yes—
673C22C2×C3×#12011yescharacteristic
674C22C2×C3×#12111yescharacteristic
675C22C2×C3×#12711yescharacteristic
676C22C3×#57712yes—
677C22C3×#57812yes—
678C4—42no—
679C4—42no—
680C4—44no—
681C4—44no—
682C4—82no—
683C4C3×#39214yes—
684C4C2×C3×#12011yescharacteristic
685C4C2×C3×#12011yescharacteristic
686C4C2×C3×#12111yescharacteristic
687C4C2×C3×#12111yescharacteristic
688C3#2342711yescharacteristic, direct product factor, Sylow
689C2—24no—
690C2—82no—
691C2—82no—
692C2C2×C3×#39211yescharacteristic
693C2C3×#301312yes—
694C2C3×#304612yes—
695C2C3×#315411yescharacteristic
696C2C3×#315611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#135C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#137C2semidirect
3. C2×C3×#536C2semidirect
4. C2×C3×#417C2semidirect
5. C22×C3×#103C2semidirect
6. C3×#2311C2semidirect
7. C3×#2016C2semidirect
8. C3×#2015C2semidirect
9. C3×#2013C2semidirect
10. C3×#2012C2semidirect
11. C3×#1729C2semidirect
12. #23427C3direct (N × H)
50. C22×#137C2×C3semidirect
52. C2×#536C2×C3semidirect
53. C2×#417C2×C3semidirect
54. C22×#103C2×C3semidirect
55. #2311C2×C3semidirect
56. #2016C2×C3semidirect
57. #2015C2×C3semidirect
58. #2013C2×C3semidirect
59. #2012C2×C3semidirect
60. #1729C2×C3semidirect
688. C3#23427direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C22×C3×#1352
C2×C3×#5362
C2×C3×#4172
C22×C3×#1032
C3×#23112
C3×#20162
C3×#20152
C3×#20132
C3×#20122
C3×#17292
#234273