Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C11×#2868 | C2 |
| hypercenter | #2868 | D11 |
| hypocenter | C11 | #36644 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2868 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10623256 | C2 | semidirect |
| 2. #13077011 | C2 | semidirect |
| 3. #13076974 | C2 | semidirect |
| 4. #13076962 | C2 | semidirect |
| 5. #13071178 | C2 | semidirect |
| 6. C43×D11 | C2 | semidirect |
| 7. C11×#2868 | C2 | semidirect |
| 45. C42×D11 | D4 | semidirect |
| 66. C42×C11 | #41 | semidirect |
| 72. #2868 | D11 | semidirect |
| 96. C4×D11 | #127 | semidirect |
| 120. C4×C11 | #532 | semidirect |
| 173. C42 | #4343 | semidirect |
| 174. C11 | #36644 | semidirect |
| 204. C4 | #10623256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10623256 | 2 |
| #13077011 | 2 |
| #13076974 | 2 |
| #13076962 | 2 |
| #13071178 | 2 |
| C43×D11 | 2 |
| C11×#2868 | 2 |
| #36644 | 11 |