Subgroups — #13096147

Order 1568.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#11716064	C₂	1	1	yes	maximal, characteristic
3	C₇⋊(C₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	C₇²×Q₈	—	2	1	no	—
5	#87648	—	2	1	no	—
6	C₇²×C₈	C₂²	1	1	yes	characteristic
7	#6403	—	7	8	no	maximal
8	C₄×C₇²	—	4	1	no	—
9	C₄×C₇²	D₄	1	1	yes	characteristic
10	C₇⋊Dic₇	—	4	1	no	—
11	C₇×Q₁₆	D₇	1	8	yes	—
12	Dic₂₈	—	7	8	no	—
13	C₇⋊C₁₆	—	7	8	no	—
14	C₂×C₇²	D₈	1	1	yes	characteristic
15	C₇×Q₈	—	2	8	no	—
16	Dic₁₄	—	14	8	no	—
17	C₇×C₈	C₂×D₇	1	8	yes	—
18	C₇²	Q₃₂	1	1	yes	characteristic, complemented, Sylow
19	Q₃₂	—	49	1	no	Sylow
20	C₄×C₇	—	4	8	no	—
21	C₄×C₇	C₂²⋊D₇	1	8	yes	—
22	Dic₇	—	28	8	no	—
23	Q₁₆	—	49	1	no	—
24	Q₁₆	C₇⋊D₇	1	1	yes	characteristic
25	C₁₆	—	49	1	no	—
26	C₂×C₇	#1141	1	8	yes	—
27	Q₈	—	2	1	no	—
28	Q₈	—	98	1	no	—
29	C₈	C₂×C₇⋊D₇	1	1	yes	characteristic
30	C₇	#6403	1	8	yes	complemented
31	C₄	—	4	1	no	—
32	C₄	—	196	1	no	—
33	C₄	C₂²⋊(C₇⋊D₇)	1	1	yes	characteristic
34	C₂	#11716071	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₇²	Q₃₂	semidirect
30. C₇	#6403	semidirect

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