Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
240 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 77 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. #13067502 | C2 | semidirect |
| 3. C8×D88 | C2 | semidirect |
| 4. #13066690 | C2 | semidirect |
| 5. #13066578 | C2 | semidirect |
| 6. #13066578 | C2 | semidirect |
| 7. C11×#1312 | C2 | semidirect |
| 64. D88 | M16 | semidirect |
| 76. #1312 | D11 | semidirect |
| 180. C11 | #12073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D176 | 2 |
| #13067502 | 2 |
| C8×D88 | 2 |
| #13066690 | 2 |
| #13066578 | 2 |
| C11×#1312 | 2 |
| #12073 | 11 |