Finite Group DatabasebetaFinite Group Databasebeta← C19×ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) #45692497
Order 33516.
132 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C72 | C32×C19 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C19 | C32 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C19 | |
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 |
|---|---|
| C22×C7×C19×ΓL(1,𝔽8) | 3 |
| C19×C22⋊#3861 | 3 |
| C7×C19×C22⋊ΓL(1,𝔽8) | 3 |
| C19×C22⋊#3862 | 3 |
| C19×ΓL(1,𝔽8)2 | 4 |
| C3×C19×C22⋊ΓL(1,𝔽8) | 7 |
| A4×C19×ΓL(1,𝔽8) | 7 |
| ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) | 19 |