Subgroups — #19149676

Order 5536.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₉₂	C₂	1	6	yes	maximal, complemented
2	C₄²×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₇₃	C₂²	1	4	yes	—
4	D₆₉₂	—	2	12	no	—
5	C₂×C₄×C₁₇₃	C₂²	1	3	yes	—
6	C₂²×C₁₇₃	C₂³	1	1	yes	characteristic
7	C₂×D₁₇₃	—	2	12	no	—
8	C₄×C₁₇₃	D₄	1	6	yes	complemented
9	C₂×C₁₇₃	C₂×D₄	1	3	yes	—
10	D₁₇₃	—	4	4	no	—
11	C₁₇₃	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	173	1	no	maximal, Sylow
13	C₂×D₄	—	173	6	no	—
14	C₄²	D₁₇₃	1	1	yes	characteristic, complemented
15	C₂³	—	173	4	no	—
16	D₄	—	346	12	no	—
17	C₂×C₄	C₂×D₁₇₃	1	3	yes	—
18	C₂²	—	346	12	no	—
19	C₂²	C₂²×D₁₇₃	1	1	yes	characteristic
20	C₄	D₆₉₂	1	6	yes	complemented
21	C₂	—	692	4	no	—
22	C₂	C₂×D₆₉₂	1	3	yes	—

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