Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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. #13079259 | C2 | semidirect |
| 2. #13070776 | C2 | semidirect |
| 3. #13070771 | C2 | semidirect |
| 4. #13070717 | C2 | semidirect |
| 5. #13070702 | C2 | semidirect |
| 6. #13070650 | C2 | semidirect |
| 7. #13070649 | C2 | semidirect |
| 8. #13070374 | C2 | semidirect |
| 9. C11×#2215 | C2 | semidirect |
| 109. #2215 | D11 | semidirect |
| 254. C11 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079259 | 2 |
| #13070776 | 2 |
| #13070771 | 2 |
| #13070717 | 2 |
| #13070702 | 2 |
| #13070650 | 2 |
| #13070649 | 2 |
| #13070374 | 2 |
| C11×#2215 | 2 |
| #33825 | 11 |