Subgroups — #20295955

Order 6976.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812770	C₂	1	2	yes	maximal
2	C₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#13182039	—	2	2	no	—
4	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
5	#13182004	C₄	1	1	yes	characteristic
6	C₁₆×C₁₀₉	C₄	1	1	yes	characteristic
7	C₄×D₁₀₉	D₄	1	1	yes	characteristic
8	#11724786	—	4	2	no	—
9	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	#11724784	Q₈	1	1	yes	characteristic
11	C₂×D₁₀₉	Q₁₆	1	1	yes	characteristic
12	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
13	Dic₁₀₉	D₈	1	1	yes	characteristic
14	C₂×C₁₀₉	#107	1	1	yes	characteristic
15	D₁₀₉	—	2	1	no	—
16	C₁₀₉	#368	1	1	yes	characteristic, complemented, Sylow
17	#368	—	109	1	no	maximal, Sylow
18	C₂×C₁₆	—	109	1	no	—
19	#108	—	109	2	no	—
20	M₁₆	—	218	2	no	—
21	C₂×C₈	—	109	1	no	—
22	C₁₆	—	109	1	no	—
23	C₁₆	#89137	1	1	yes	characteristic
24	C₂×C₄	—	109	1	no	—
25	C₈	—	109	1	no	—
26	C₈	—	436	2	no	—
27	C₈	C₂×#89137	1	1	yes	characteristic
28	C₂²	—	109	1	no	—
29	C₄	—	109	1	no	—
30	C₄	C₄⋊#89137	1	1	yes	characteristic
31	C₂	—	218	1	no	—
32	C₂	#16812768	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₁₀₉	#368	semidirect