Subgroups — #11763741

Order 1088.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63214	C₂	1	1	yes	maximal, characteristic
2	#10587467	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×C₁₇	C₄	1	1	yes	characteristic
4	#63214	C₄	1	1	yes	characteristic
5	#63214	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₇	C₈	1	1	yes	characteristic
7	C₈×C₁₇	C₈	1	1	yes	characteristic
8	C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₇	C₁₆	1	1	yes	characteristic
10	C₄×C₁₇	C₁₆	1	1	yes	characteristic
11	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
12	M₆₄	—	17	1	no	maximal, Sylow
13	C₂×C₁₇	—	2	1	no	—
14	C₂×C₁₇	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₆	—	17	1	no	—
16	C₃₂	—	17	2	no	—
17	C₁₇	M₆₄	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₈	#595	1	1	yes	characteristic
19	C₁₆	—	17	1	no	—
20	C₁₆	—	17	1	no	—
21	C₂×C₄	#3624	1	1	yes	characteristic
22	C₈	#3624	1	1	yes	characteristic
23	C₈	C₂×#595	1	1	yes	characteristic
24	C₂²	#63216	1	1	yes	characteristic
25	C₄	#63216	1	1	yes	characteristic
26	C₄	C₂×#3624	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×#63216	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #10587467	C₂	semidirect
17. C₁₇	M₆₄	semidirect

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