Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
280 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)2×D17 |
| commutator, cosocle, hypocenter | C72×C17 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C17 | C2×C32 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C2 | |
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 |
|---|---|
| C2×C17×ΓL(1,𝔽8)2 | 2 |
| ΓL(1,𝔽8)2×D17 | 2 |
| C2×D17×#3862 | 3 |
| C2×D17×#3861 | 3 |
| C2×C7×ΓL(1,𝔽8)×D17 | 3 |
| C2×C3×ΓL(1,𝔽8)×D17 | 7 |
| C22×ΓL(1,𝔽8)2 | 17 |