Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D352 |
| commutator, cosocle | C11×C32 | C23 |
| Frattini | C32 | C22×D11 |
| Fitting | C11×M128 | C2 |
| socle | C2×C11 | C2×D32 |
| hypercenter | M128 | D11 |
| hypocenter | C11 | #13742 |
| LCS | G ▷ C11×C32 ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ M128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13070925 | C2 | semidirect |
| 2. C2×D352 | C2 | semidirect |
| 3. #13066832 | C2 | semidirect |
| 4. D704 | C2 | semidirect |
| 5. C11×M128 | C2 | semidirect |
| 9. Dic176 | C22 | semidirect |
| 13. D352 | C22 | semidirect |
| 14. C11×C64 | C22 | semidirect |
| 40. M128 | D11 | semidirect |
| 59. C64 | C2×D11 | semidirect |
| 91. C11 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070925 | 2 |
| C2×D352 | 2 |
| #13066832 | 2 |
| D704 | 2 |
| C11×M128 | 2 |
| #13742 | 11 |