Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. C2×#10622532 | C2 | semidirect |
| 2. #13080375 | C2 | semidirect |
| 3. #13070866 | C2 | semidirect |
| 4. #13070703 | C2 | semidirect |
| 5. #13070656 | C2 | semidirect |
| 6. #13070542 | C2 | semidirect |
| 7. C16×D44 | C2 | semidirect |
| 8. C4×C11×Q32 | C2 | semidirect |
| 44. C11×Q32 | D4 | semidirect |
| 97. C4×Q32 | D11 | semidirect |
| 153. C4×C11 | #508 | semidirect |
| 172. Q32 | D44 | semidirect |
| 223. C11 | #33853 | semidirect |
| 259. C4 | #10622532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622532 | 2 |
| #13080375 | 2 |
| #13070866 | 2 |
| #13070703 | 2 |
| #13070656 | 2 |
| #13070542 | 2 |
| C16×D44 | 2 |
| C4×C11×Q32 | 2 |
| #33853 | 11 |