Finite Group DatabasebetaFinite Group Databasebeta← C4×ΓL(1,𝔽8)×GO+(4,𝔽2) #72217684
Order 6048.
656 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
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.
| subgroup | index |
|---|---|
| C4×C7×GO+(4,𝔽2) | 3 |
| ΓL(1,𝔽8)×#3773 | 2 |
| ΓL(1,𝔽8)×D32⋊C4 | 2 |
| C2×ΓL(1,𝔽8)×GO+(4,𝔽2) | 2 |
| C4×D32×ΓL(1,𝔽8) | 2 |
| C4×ΓL(1,𝔽8)×#157 | 2 |
| C3×C4×GO+(4,𝔽2) | 7 |
| C4×D4×ΓL(1,𝔽8) | 9 |