Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1078 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 259 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D11 |
| commutator, socle, prime radical, cosocle | C24×C11 | C24 |
| Fitting | C11×#1444 | C2 |
| hypercenter | #1444 | D11 |
| hypocenter | C11 | #17295 |
| LCS | G ▷ C24×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ #1444 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 30. C11×#95 | Q8 | semidirect |
| 148. #95 | Dic22 | semidirect |
| 185. C11 | #17295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13066886 | 2 |
| #13066885 | 2 |
| #13066878 | 2 |
| #13066869 | 2 |
| C11×#1444 | 2 |
| #17295 | 11 |