Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
642 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #13079075 | C2 | semidirect |
| 3. C2×#10622307 | C2 | semidirect |
| 4. #13069456 | C2 | semidirect |
| 5. #13067287 | C2 | semidirect |
| 6. #13067068 | C2 | semidirect |
| 7. C11×#1278 | C2 | semidirect |
| 101. C11×M16 | D8 | semidirect |
| 129. #1278 | D11 | semidirect |
| 292. M16 | D88 | semidirect |
| 310. C11 | #10168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079536 | 2 |
| #13079075 | 2 |
| C2×#10622307 | 2 |
| #13069456 | 2 |
| #13067287 | 2 |
| #13067068 | 2 |
| C11×#1278 | 2 |
| #10168 | 11 |