Finite Group Databasebeta

← C67×#14920 #30694171

Subgroups — C67×#14920 #30694171

Order 17152.

1846 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C67C211yesmaximal, characteristic
2C2×#385×C67C211yesmaximal, characteristic
3C2×#380×C67C211yesmaximal, characteristic
4C22×#95×C67C211yesmaximal, characteristic
5C67×#1445C212yesmaximal, complemented
6C67×#1442C212yesmaximal, complemented
7C67×#1441C212yesmaximal, complemented
8C67×#1441C212yesmaximal, complemented
9C67×C22⋊#95C211yesmaximal, characteristic
10C67×C22⋊#95C211yesmaximal, characteristic
11C67×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C67C2211yescharacteristic
13C24×C4×C67C2211yescharacteristic
14C24×C4×C67C2211yescharacteristic
15C22×C4⋊C4×C67C2211yescharacteristic
16C22×C4⋊C4×C67C2212yes—
17C22×C4⋊C4×C67C2212yes—
18C22×C4⋊C4×C67C2211yescharacteristic
19C22×C22⋊C4×C67C2211yescharacteristic
20C22×C22⋊C4×C67C2211yescharacteristic
21C22×C22⋊C4×C67C2211yescharacteristic
22C22×C22⋊C4×C67C2211yescharacteristic
23#385×C67—24no—
24#385×C67—24no—
25#380×C67—24no—
26C2×#95×C67—24no—
27C2×#95×C67C2212yes—
28C2×#95×C67C2212yes—
29C2×#95×C67C2212yes—
30C2×#95×C67C2211yescharacteristic
31C2×#95×C67C2212yes—
32C2×#95×C67C2211yescharacteristic
33C2×#95×C67C2212yes—
34C2×#95×C67C2212yes—
35C2×#95×C67C2212yes—
36C2×#95×C67C2212yes—
37C2×#95×C67C2212yes—
38C2×#95×C67C2212yes—
39C25×C67C2311yescharacteristic
40C23×C4×C67—22no—
41C23×C4×C67—22no—
42C23×C4×C67—22no—
43C23×C4×C67—22no—
44C23×C4×C67—22no—
45C23×C4×C67—24no—
46C23×C4×C67—24no—
47C23×C4×C67—22no—
48C23×C4×C67—22no—
49C23×C4×C67—42no—
50C23×C4×C67—42no—
51C23×C4×C67—42no—
52C23×C4×C67—42no—
53C23×C4×C67D414yes—
54C23×C4×C67Q814yes—
55C23×C4×C67C2311yescharacteristic
56C23×C4×C67C2311yescharacteristic
57C23×C4×C67C2312yes—
58C23×C4×C67C2312yes—
59C23×C4×C67C2311yescharacteristic
60C23×C4×C67C2311yescharacteristic
61C23×C4×C67C2311yescharacteristic
62C23×C4×C67C2312yes—
63C23×C4×C67C2312yes—
64C23×C4×C67C2311yescharacteristic
65C2×C4⋊C4×C67—24no—
66C2×C4⋊C4×C67—24no—
67C2×C4⋊C4×C67—22no—
68C2×C4⋊C4×C67—22no—
69C2×C4⋊C4×C67—24no—
70C2×C4⋊C4×C67—24no—
71C2×C4⋊C4×C67—24no—
72C2×C4⋊C4×C67—42no—
73C2×C4⋊C4×C67—42no—
74C2×C4⋊C4×C67—42no—
75C2×C22⋊C4×C67—22no—
76C2×C22⋊C4×C67—22no—
77C2×C22⋊C4×C67—22no—
78C2×C22⋊C4×C67—22no—
79C2×C22⋊C4×C67—22no—
80C2×C22⋊C4×C67—22no—
81C2×C22⋊C4×C67—22no—
82C2×C22⋊C4×C67—22no—
83C2×C22⋊C4×C67—22no—
84C2×C22⋊C4×C67—22no—
85C2×C22⋊C4×C67D414yes—
86C2×C22⋊C4×C67Q814yes—
87#95×C67—24no—
88#95×C67—24no—
89#95×C67—24no—
90#95×C67—22no—
91#95×C67—22no—
92#95×C67—24no—
93#95×C67—24no—
94#95×C67—42no—
95#95×C67—42no—
96#95×C67—42no—
97#95×C67—42no—
98#95×C67—42no—
99C24×C67—22no—
100C24×C67—22no—
101C24×C67—22no—
102C24×C67—22no—
103C24×C67C2×D412yes—
104C24×C67C2×D412yes—
105C24×C67C2×Q812yes—
106C24×C67C2×Q812yes—
107C24×C67#4112yes—
108C24×C67#4112yes—
109C24×C67#4112yes—
110C24×C67C2411yescharacteristic
111C22×C4×C67—21no—
112C22×C4×C67—21no—
113C22×C4×C67—22no—
114C22×C4×C67—28no—
115C22×C4×C67—28no—
116C22×C4×C67—28no—
117C22×C4×C67—21no—
118C22×C4×C67—21no—
119C22×C4×C67—22no—
120C22×C4×C67—21no—
121C22×C4×C67—22no—
122C22×C4×C67—22no—
123C22×C4×C67—21no—
124C22×C4×C67—21no—
125C22×C4×C67—22no—
126C22×C4×C67—22no—
127C22×C4×C67—22no—
128C22×C4×C67—22no—
129C22×C4×C67—22no—
130C22×C4×C67—21no—
131C22×C4×C67—22no—
132C22×C4×C67—22no—
133C22×C4×C67—22no—
134C22×C4×C67—22no—
135C22×C4×C67—22no—
136C22×C4×C67—22no—
137C22×C4×C67—22no—
138C22×C4×C67—22no—
139C22×C4×C67—22no—
140C22×C4×C67—22no—
141C22×C4×C67—22no—
142C22×C4×C67—22no—
143C22×C4×C67—22no—
144C22×C4×C67—22no—
145C22×C4×C67—22no—
146C22×C4×C67—22no—
147C22×C4×C67—28no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—22no—
151C22×C4×C67—21no—
152C22×C4×C67—21no—
153C22×C4×C67—21no—
154C22×C4×C67—21no—
155C22×C4×C67—22no—
156C22×C4×C67—22no—
157C22×C4×C67—22no—
158C22×C4×C67—22no—
159C22×C4×C67—22no—
160C22×C4×C67—22no—
161C22×C4×C67—22no—
162C22×C4×C67—22no—
163C22×C4×C67—22no—
164C22×C4×C67—22no—
165C22×C4×C67—44no—
166C22×C4×C67—48no—
167C22×C4×C67—48no—
168C22×C4×C67—48no—
169C22×C4×C67—48no—
170C22×C4×C67—48no—
171C22×C4×C67—44no—
172C22×C4×C67—44no—
173C22×C4×C67—44no—
174C22×C4×C67—48no—
175C22×C4×C67—44no—
176C22×C4×C67C2×D414yes—
177C22×C4×C67C2×D412yes—
178C22×C4×C67C2×D412yes—
179C22×C4×C67C2×Q812yes—
180C22×C4×C67C2×Q812yes—
181C22×C4×C67C2×Q814yes—
182C22×C4×C67#4114yes—
183C22×C4×C67#4114yes—
184C4⋊C4×C67—48no—
185C4⋊C4×C67—48no—
186C4⋊C4×C67—44no—
187C4⋊C4×C67—44no—
188C22⋊C4×C67—28no—
189C22⋊C4×C67—28no—
190C22⋊C4×C67—44no—
191C22⋊C4×C67—44no—
192C23×C67—22no—
193C23×C67—22no—
194C23×C67—24no—
195C23×C67—24no—
196C23×C67—22no—
197C23×C67—22no—
198C23×C67—24no—
199C23×C67—24no—
200C23×C67—24no—
201C23×C67—24no—
202C23×C67—24no—
203C23×C67—24no—
204C23×C67—24no—
205C23×C67—24no—
206C23×C67—24no—
207C23×C67—24no—
208C23×C67#12114yes—
209C23×C67C22⋊Q814yes—
210C23×C67C22⋊Q814yes—
211C23×C67#12314yes—
212C23×C67#12514yes—
213C23×C67#12514yes—
214C23×C67C4⋊Q814yes—
215C23×C67C22×D411yescharacteristic
216C23×C67C22×D411yescharacteristic
217C23×C67C22×Q811yescharacteristic
218C23×C67C22×Q811yescharacteristic
219C23×C67C2×#4111yescharacteristic
220C23×C67C2×#4111yescharacteristic
221C23×C67C2×#4111yescharacteristic
222C23×C67C2×#4112yes—
223C23×C67C2×#4112yes—
224C23×C67H(5,𝔽2)12yes—
225C23×C67H(5,𝔽2)12yes—
226C2×C4×C67—22no—
227C2×C4×C67—22no—
228C2×C4×C67—24no—
229C2×C4×C67—24no—
230C2×C4×C67—22no—
231C2×C4×C67—22no—
232C2×C4×C67—22no—
233C2×C4×C67—24no—
234C2×C4×C67—24no—
235C2×C4×C67—22no—
236C2×C4×C67—24no—
237C2×C4×C67—22no—
238C2×C4×C67—24no—
239C2×C4×C67—24no—
240C2×C4×C67—24no—
241C2×C4×C67—24no—
242C2×C4×C67—24no—
243C2×C4×C67—24no—
244C2×C4×C67—24no—
245C2×C4×C67—24no—
246C2×C4×C67—416no—
247C2×C4×C67—416no—
248C2×C4×C67—416no—
249C2×C4×C67—42no—
250C2×C4×C67—41no—
251C2×C4×C67—41no—
252C2×C4×C67—42no—
253C2×C4×C67—41no—
254C2×C4×C67—42no—
255C2×C4×C67—41no—
256C2×C4×C67—42no—
257C2×C4×C67—42no—
258C2×C4×C67—42no—
259C2×C4×C67—42no—
260C2×C4×C67—42no—
261C2×C4×C67—42no—
262C2×C4×C67—42no—
263C2×C4×C67—42no—
264C2×C4×C67—42no—
265C2×C4×C67—42no—
266C2×C4×C67—42no—
267C2×C4×C67—42no—
268C2×C4×C67—42no—
269C2×C4×C67—41no—
270C2×C4×C67—41no—
271C2×C4×C67—42no—
272C2×C4×C67—41no—
273C2×C4×C67—41no—
274C2×C4×C67—42no—
275C2×C4×C67—41no—
276C2×C4×C67—41no—
277C2×C4×C67—42no—
278C2×C4×C67—42no—
279C2×C4×C67—42no—
280C2×C4×C67—42no—
281C2×C4×C67—42no—
282C2×C4×C67—42no—
283C2×C4×C67—42no—
284C2×C4×C67—42no—
285C2×C4×C67—42no—
286C2×C4×C67#12314yes—
287C22×C67—28no—
288C22×C67—24no—
289C22×C67—24no—
290C22×C67—24no—
291C22×C67—24no—
292C22×C67—24no—
293C22×C67—28no—
294C22×C67—24no—
295C22×C67—28no—
296C22×C67—28no—
297C22×C67#39818yes—
298C22×C67C2×#12111yescharacteristic
299C22×C67C2×C22⋊Q811yescharacteristic
300C22×C67C2×C22⋊Q811yescharacteristic
301C22×C67C2×#12311yescharacteristic
302C22×C67C2×#12311yescharacteristic
303C22×C67#52511yescharacteristic
304C22×C67C2×#12511yescharacteristic
305C22×C67C2×#12511yescharacteristic
306C22×C67#52912yes—
307C22×C67C2×C4⋊Q811yescharacteristic
308C22×C67#53312yes—
309C22×C67#53411yescharacteristic
310C22×C67#53511yescharacteristic
311C22×C67#53812yes—
312C22×C67#54312yes—
313C22×C67#54612yes—
314C22×C67#54612yes—
315C22×C67#55112yes—
316C22×C67#55112yes—
317C22×C67#55312yes—
318C22×C67#55312yes—
319C22×C67#55412yes—
320C22×C67#55412yes—
321C4×C67—24no—
322C4×C67—42no—
323C4×C67—44no—
324C4×C67—44no—
325C4×C67—42no—
326C4×C67—44no—
327C4×C67—42no—
328C4×C67—81no—
329C4×C67—81no—
330C4×C67—82no—
331#14920C6711yesmaximal, characteristic, direct product factor, Sylow
332C2×C67—28no—
333C2×C67C2×#39811yescharacteristic
334C2×C67#241111yescharacteristic
335C2×C67#241211yescharacteristic
336C2×C67#244412yes—
337C2×C67#248711yescharacteristic
338C2×C67#250512yes—
339C2×C67#254912yes—
340C2×C67#256912yes—
341C2×C67#257911yescharacteristic
342C2×C67#262611yescharacteristic
343C2×C67#285511yescharacteristic
344C2×#385C2×C6711yescharacteristic
345C2×#385C2×C6711yescharacteristic
346C2×#380C2×C6711yescharacteristic
347C22×#95C2×C6711yescharacteristic
348#1445C2×C6712yescomplemented
349#1442C2×C6712yescomplemented
350#1441C2×C6712yescomplemented
351#1441C2×C6712yescomplemented
352C22⋊#95C2×C6711yescharacteristic
353C22⋊#95C2×C6711yescharacteristic
354C22⋊#95C2×C6711yescharacteristic
355C67#1492011yescharacteristic, direct product factor, Sylow
356C24×C4C22×C6711yescharacteristic
357C24×C4C22×C6711yescharacteristic
358C24×C4C22×C6711yescharacteristic
359C22×C4⋊C4C22×C6711yescharacteristic
360C22×C4⋊C4C22×C6712yes—
361C22×C4⋊C4C22×C6712yes—
362C22×C4⋊C4C22×C6711yescharacteristic
363C22×C22⋊C4C22×C6711yescharacteristic
364C22×C22⋊C4C22×C6711yescharacteristic
365C22×C22⋊C4C22×C6711yescharacteristic
366C22×C22⋊C4C22×C6711yescharacteristic
367#385—24no—
368#385—24no—
369#380—24no—
370C2×#95—24no—
371C2×#95C22×C6712yes—
372C2×#95C22×C6712yes—
373C2×#95C22×C6711yescharacteristic
374C2×#95C22×C6712yes—
375C2×#95C22×C6712yes—
376C2×#95C22×C6712yes—
377C2×#95C22×C6711yescharacteristic
378C2×#95C22×C6712yes—
379C2×#95C22×C6712yes—
380C2×#95C22×C6712yes—
381C2×#95C22×C6712yes—
382C2×#95C22×C6712yes—
383C25C23×C6711yescharacteristic
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4D4×C6714yes—
398C23×C4Q8×C6714yes—
399C23×C4C23×C6711yescharacteristic
400C23×C4C23×C6711yescharacteristic
401C23×C4C23×C6712yes—
402C23×C4C23×C6712yes—
403C23×C4C23×C6711yescharacteristic
404C23×C4C23×C6711yescharacteristic
405C23×C4C23×C6711yescharacteristic
406C23×C4C23×C6712yes—
407C23×C4C23×C6712yes—
408C23×C4C23×C6711yescharacteristic
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4D4×C6714yes—
430C2×C22⋊C4Q8×C6714yes—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—22no—
435#95—22no—
436#95—24no—
437#95—24no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24C2×D4×C6712yes—
448C24C2×D4×C6712yes—
449C24C2×Q8×C6712yes—
450C24C2×Q8×C6712yes—
451C24#41×C6712yes—
452C24#41×C6712yes—
453C24#41×C6712yes—
454C24C24×C6711yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
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—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4C2×D4×C6712yes—
521C22×C4C2×D4×C6714yes—
522C22×C4C2×D4×C6712yes—
523C22×C4C2×Q8×C6712yes—
524C22×C4C2×Q8×C6712yes—
525C22×C4C2×Q8×C6714yes—
526C22×C4#41×C6714yes—
527C22×C4#41×C6714yes—
528C4⋊C4—48no—
529C4⋊C4—48no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C22⋊C4—28no—
533C22⋊C4—28no—
534C22⋊C4—44no—
535C22⋊C4—44no—
536C23—22no—
537C23—22no—
538C23—24no—
539C23—24no—
540C23—22no—
541C23—22no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23#121×C6714yes—
553C23C22⋊Q8×C6714yes—
554C23C22⋊Q8×C6714yes—
555C23#123×C6714yes—
556C23#125×C6714yes—
557C23#125×C6714yes—
558C23C4⋊Q8×C6714yes—
559C23C22×D4×C6711yescharacteristic
560C23C22×D4×C6711yescharacteristic
561C23C22×Q8×C6711yescharacteristic
562C23C22×Q8×C6711yescharacteristic
563C23C2×#41×C6711yescharacteristic
564C23C2×#41×C6711yescharacteristic
565C23C2×#41×C6711yescharacteristic
566C23C2×#41×C6712yes—
567C23C2×#41×C6712yes—
568C23H(5,𝔽2)×C6712yes—
569C23H(5,𝔽2)×C6712yes—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—416no—
591C2×C4—416no—
592C2×C4—416no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—42no—
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—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4#123×C6714yes—
631C22—28no—
632C22—28no—
633C22—28no—
634C22—24no—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—28no—
640C22—24no—
641C22#398×C6718yes—
642C22C2×#121×C6711yescharacteristic
643C22C2×C22⋊Q8×C6711yescharacteristic
644C22C2×C22⋊Q8×C6711yescharacteristic
645C22C2×#123×C6711yescharacteristic
646C22C2×#123×C6711yescharacteristic
647C22#525×C6711yescharacteristic
648C22C2×#125×C6711yescharacteristic
649C22C2×#125×C6711yescharacteristic
650C22#529×C6712yes—
651C22C2×C4⋊Q8×C6711yescharacteristic
652C22#533×C6712yes—
653C22#534×C6711yescharacteristic
654C22#535×C6711yescharacteristic
655C22#538×C6712yes—
656C22#543×C6712yes—
657C22#546×C6712yes—
658C22#546×C6712yes—
659C22#551×C6712yes—
660C22#551×C6712yes—
661C22#553×C6712yes—
662C22#553×C6712yes—
663C22#554×C6712yes—
664C22#554×C6712yes—
665C4—24no—
666C4—42no—
667C4—44no—
668C4—44no—
669C4—42no—
670C4—44no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—82no—
675C2—28no—
676C2C2×#398×C6711yescharacteristic
677C2C67×#241111yescharacteristic
678C2C67×#241211yescharacteristic
679C2C67×#244412yes—
680C2C67×#248711yescharacteristic
681C2C67×#250512yes—
682C2C67×#254912yes—
683C2C67×#256912yes—
684C2C67×#257911yescharacteristic
685C2C67×#262611yescharacteristic
686C2C67×#285511yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutator, Frattini, cosocleC24C24×C67
prime radicalC25×C67C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
5. C67×#1445C2semidirect
6. C67×#1442C2semidirect
7. C67×#1441C2semidirect
8. C67×#1441C2semidirect
331. #14920C67direct (N × H)
348. #1445C2×C67semidirect
349. #1442C2×C67semidirect
350. #1441C2×C67semidirect
351. #1441C2×C67semidirect
355. C67#14920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#385×C672
C2×#380×C672
C22×#95×C672
C67×#14452
C67×#14422
C67×#14412
C67×C22⋊#952
#1492067