Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 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×#2840 | C2 |
| hypercenter | #2840 | D11 |
| hypocenter | C11 | #36675 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13076807 | C2 | semidirect |
| 2. #13076700 | C2 | semidirect |
| 3. #13076613 | C2 | semidirect |
| 4. #13071898 | C2 | semidirect |
| 5. #13071833 | C2 | semidirect |
| 6. #13071115 | C2 | semidirect |
| 7. C11×#2840 | C2 | semidirect |
| 9. C22×#4343 | C22 | semidirect |
| 11. C2×Q8×Dic11 | C22 | semidirect |
| 16. #10622844 | C22 | semidirect |
| 17. #10622842 | C22 | semidirect |
| 24. #10622287 | C22 | semidirect |
| 25. #10622285 | C22 | semidirect |
| 26. #10622279 | C22 | semidirect |
| 27. #10622273 | C22 | semidirect |
| 28. #10622261 | C22 | semidirect |
| 58. C24×C11 | #41 | semidirect |
| 86. #2840 | D11 | semidirect |
| 188. C24 | #4343 | semidirect |
| 215. C11 | #36675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076807 | 2 |
| #13076700 | 2 |
| #13076613 | 2 |
| #13071898 | 2 |
| #13071833 | 2 |
| #13071115 | 2 |
| C11×#2840 | 2 |
| #36675 | 11 |