Subgroups — D₁₈₇₅₂ #49156998

Order 37504.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₃₇₆	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₆₈₈	—	2	2	no	—
4	C₃₂×C₂₉₃	C₂²	1	1	yes	characteristic
5	D₂₃₄₄	—	4	2	no	—
6	C₁₆×C₂₉₃	D₄	1	1	yes	characteristic
7	D₁₁₇₂	—	8	2	no	—
8	C₈×C₂₉₃	D₈	1	1	yes	characteristic
9	C₂×D₂₉₃	—	16	2	no	—
10	C₄×C₂₉₃	D₁₆	1	1	yes	characteristic
11	C₂×C₂₉₃	D₃₂	1	1	yes	characteristic
12	D₂₉₃	—	32	2	no	—
13	C₂₉₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
14	D₆₄	—	293	1	no	maximal, Sylow
15	D₃₂	—	293	2	no	—
16	C₆₄	D₂₉₃	1	1	yes	characteristic, complemented
17	D₁₆	—	586	2	no	—
18	C₃₂	C₂×D₂₉₃	1	1	yes	characteristic
19	D₈	—	1172	2	no	—
20	C₁₆	D₁₁₇₂	1	1	yes	characteristic
21	D₄	—	2344	2	no	—
22	C₈	D₂₃₄₄	1	1	yes	characteristic
23	C₂²	—	4688	2	no	—
24	C₄	D₄₆₈₈	1	1	yes	characteristic
25	C₂	—	9376	2	no	—
26	C₂	D₉₃₇₆	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.