Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4886 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 4886 conjugacy classes of subgroups — too many to draw. Only its 907 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D11 |
| commutator, cosocle | C23×C11 | C25 |
| Frattini | C23 | C24×D11 |
| Fitting | C22×C11×#95 | C2 |
| socle | C24×C11 | C24 |
| hypercenter | C22×#95 | D11 |
| hypocenter | C11 | C2×#2656 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#66983 | C2 | semidirect |
| 2. #13074718 | C2 | direct (N × H) |
| 3. C2×#10622290 | C2 | semidirect |
| 4. C2×#10622284 | C2 | semidirect |
| 5. C22×C11×#95 | C2 | semidirect |
| 10. C2×#66983 | C22 | semidirect |
| 14. C2×C11×#95 | C22 | semidirect |
| 15. #10622290 | C22 | semidirect |
| 16. #10622284 | C22 | semidirect |
| 20. C23×C4×C11 | D4 | semidirect |
| 49. C22×C4×C11 | C2×D4 | semidirect |
| 64. C22×#95 | D11 | semidirect |
| 99. C2×#95 | C2×D11 | semidirect |
| 125. C23×C4 | D44 | semidirect |
| 135. C2×C11 | #2656 | semidirect |
| 160. C22×C4 | C2×D44 | semidirect |
| 164. C11 | C2×#2656 | semidirect |
| 207. C2 | #13074718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66983 | 2 |
| #13074718 | 2 |
| C2×#10622290 | 2 |
| C2×#10622284 | 2 |
| C22×C11×#95 | 2 |
| C2×#2656 | 11 |