Subgroups — D₂₇₅₂ #19132808

Order 5504.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₇₆	C₂	1	2	yes	maximal, complemented
2	C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₆₈₈	—	2	2	no	—
4	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
5	D₃₄₄	—	4	2	no	—
6	C₁₆×C₄₃	D₄	1	1	yes	characteristic
7	D₁₇₂	—	8	2	no	—
8	C₈×C₄₃	D₈	1	1	yes	characteristic
9	C₂×D₄₃	—	16	2	no	—
10	C₄×C₄₃	D₁₆	1	1	yes	characteristic
11	D₆₄	—	43	1	no	maximal, Sylow
12	C₂×C₄₃	D₃₂	1	1	yes	characteristic
13	D₄₃	—	32	2	no	—
14	D₃₂	—	43	2	no	—
15	C₆₄	D₄₃	1	1	yes	characteristic, complemented
16	C₄₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
17	D₁₆	—	86	2	no	—
18	C₃₂	C₂×D₄₃	1	1	yes	characteristic
19	D₈	—	172	2	no	—
20	C₁₆	D₁₇₂	1	1	yes	characteristic
21	D₄	—	344	2	no	—
22	C₈	D₃₄₄	1	1	yes	characteristic
23	C₂²	—	688	2	no	—
24	C₄	D₆₈₈	1	1	yes	characteristic
25	C₂	—	1376	2	no	—
26	C₂	D₁₃₇₆	1	1	yes	characteristic

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