Subgroups — #14582738

Order 2752.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₆₈₈	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₇₂	—	2	1	no	—
5	D₃₄₄	—	2	1	no	—
6	C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	D₁₇₂	—	4	1	no	—
8	Dic₈₆	—	4	1	no	—
9	C₈×C₄₃	D₄	1	1	yes	characteristic
10	C₂×D₄₃	—	8	1	no	—
11	C₄×C₄₃	D₈	1	1	yes	characteristic
12	Dic₄₃	—	8	1	no	—
13	C₂×C₄₃	D₁₆	1	1	yes	characteristic
14	D₄₃	—	16	1	no	—
15	SD₆₄	—	43	1	no	maximal, Sylow
16	C₄₃	SD₆₄	1	1	yes	characteristic, complemented, Sylow
17	Q₃₂	—	43	1	no	—
18	D₁₆	—	43	1	no	—
19	C₃₂	D₄₃	1	1	yes	characteristic, complemented
20	Q₁₆	—	86	1	no	—
21	D₈	—	86	1	no	—
22	C₁₆	C₂×D₄₃	1	1	yes	characteristic
23	Q₈	—	172	1	no	—
24	D₄	—	172	1	no	—
25	C₈	D₁₇₂	1	1	yes	characteristic
26	C₂²	—	344	1	no	—
27	C₄	—	344	1	no	—
28	C₄	D₃₄₄	1	1	yes	characteristic
29	C₂	—	688	1	no	—
30	C₂	D₆₈₈	1	1	yes	characteristic

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

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