Subgroups — #14523976

Order 2144.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₆₇	—	2	1	no	—
5	C₂×C₄×C₆₇	C₂²	1	1	yes	characteristic
6	C₂×Dic₆₇	—	2	1	no	—
7	C₆₇⋊C₈	C₄	1	2	yes	complemented
8	C₂²×C₆₇	D₄	1	1	yes	characteristic
9	C₄×C₆₇	—	4	1	no	—
10	C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
11	C₄×C₆₇	Q₈	1	1	yes	characteristic
12	Dic₆₇	—	4	1	no	—
13	C₂×C₆₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₆₇	D₈	1	1	yes	characteristic
15	C₂×C₆₇	Q₁₆	1	1	yes	characteristic
16	C₆₇	#107	1	1	yes	characteristic, complemented, Sylow
17	#107	—	67	1	no	maximal, Sylow
18	C₂×C₈	—	67	1	no	—
19	C₄⋊C₄	—	67	1	no	—
20	C₄⋊C₄	D₆₇	1	1	yes	characteristic
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	134	1	no	—
23	C₂×C₄	C₂×D₆₇	1	1	yes	characteristic
24	C₈	—	67	2	no	—
25	C₂²	C₂²⋊D₆₇	1	1	yes	characteristic
26	C₄	—	4	1	no	—
27	C₄	—	268	1	no	—
28	C₄	Dic₁₃₄	1	1	yes	characteristic
29	C₄	C₄×D₆₇	1	1	yes	characteristic
30	C₂	Dic₆₇⋊C₄	1	1	yes	characteristic
31	C₂	#11761613	1	1	yes	characteristic
32	C₂	#11761618	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₆₇⋊C₈	C₄	semidirect
16. C₆₇	#107	semidirect

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