Subgroups — D₁₇₃₄₄ #46834577

Order 34688.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₇₂	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₃₃₆	—	2	2	no	—
4	C₃₂×C₂₇₁	C₂²	1	1	yes	characteristic
5	D₂₁₆₈	—	4	2	no	—
6	C₁₆×C₂₇₁	D₄	1	1	yes	characteristic
7	D₁₀₈₄	—	8	2	no	—
8	C₈×C₂₇₁	D₈	1	1	yes	characteristic
9	C₂×D₂₇₁	—	16	2	no	—
10	C₄×C₂₇₁	D₁₆	1	1	yes	characteristic
11	C₂×C₂₇₁	D₃₂	1	1	yes	characteristic
12	D₂₇₁	—	32	2	no	—
13	C₂₇₁	D₆₄	1	1	yes	characteristic, complemented, Sylow
14	D₆₄	—	271	1	no	maximal, Sylow
15	D₃₂	—	271	2	no	—
16	C₆₄	D₂₇₁	1	1	yes	characteristic, complemented
17	D₁₆	—	542	2	no	—
18	C₃₂	C₂×D₂₇₁	1	1	yes	characteristic
19	D₈	—	1084	2	no	—
20	C₁₆	D₁₀₈₄	1	1	yes	characteristic
21	D₄	—	2168	2	no	—
22	C₈	D₂₁₆₈	1	1	yes	characteristic
23	C₂²	—	4336	2	no	—
24	C₄	D₄₃₃₆	1	1	yes	characteristic
25	C₂	—	8672	2	no	—
26	C₂	D₈₆₇₂	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.