Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
456 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#10622155 | C2 | semidirect |
| 5. #13069531 | C2 | semidirect |
| 6. #13066728 | C2 | semidirect |
| 7. C11×#1378 | C2 | semidirect |
| 20. #10622522 | C4 | semidirect |
| 123. #1378 | D11 | semidirect |
| 282. C11 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622522 | 2 |
| #13077534 | 2 |
| #13070366 | 2 |
| C2×#10622155 | 2 |
| #13069531 | 2 |
| #13066728 | 2 |
| C11×#1378 | 2 |
| #13031 | 11 |