Subgroups — C₇×#368 #89410

Order 448.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₇×#108	C₂	1	2	yes	maximal
3	C₇×M₁₆	—	2	2	no	—
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₇×C₁₆	C₄	1	2	yes	—
6	#368	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₄×C₇	D₄	1	1	yes	characteristic
8	C₇×C₈	—	4	2	no	—
9	C₇×C₈	C₂×C₄	1	1	yes	characteristic
10	C₇×C₈	Q₈	1	1	yes	characteristic
11	C₂×C₁₆	C₂×C₇	1	1	yes	characteristic
12	#108	C₂×C₇	1	2	yes	—
13	C₂²×C₇	Q₁₆	1	1	yes	characteristic
14	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₇	D₈	1	1	yes	characteristic
16	M₁₆	—	2	2	no	—
17	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
18	C₁₆	C₄×C₇	1	2	yes	—
19	C₂×C₇	—	2	1	no	—
20	C₂×C₇	#107	1	1	yes	characteristic
21	C₂×C₄	C₇×D₄	1	1	yes	characteristic
22	C₈	—	4	2	no	—
23	C₈	C₂×C₄×C₇	1	1	yes	characteristic
24	C₈	C₇×Q₈	1	1	yes	characteristic
25	C₇	#368	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	C₇×Q₁₆	1	1	yes	characteristic
27	C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
28	C₄	C₇×D₈	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	C₇×#107	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. #368	C₇	direct (N × H)
25. C₇	#368	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.