Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. #13080965 | C2 | semidirect |
| 2. #13070891 | C2 | semidirect |
| 3. #13070795 | C2 | semidirect |
| 4. #13070753 | C2 | semidirect |
| 5. #13070699 | C2 | semidirect |
| 6. C16×D44 | C2 | semidirect |
| 7. D11×#366 | C2 | semidirect |
| 8. C4×C11×D16 | C2 | semidirect |
| 78. C11×C16 | #41 | semidirect |
| 85. C4×D16 | D11 | semidirect |
| 100. D44 | D16 | semidirect |
| 197. C16 | #4339 | semidirect |
| 198. C11 | #33901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13080965 | 2 |
| #13070891 | 2 |
| #13070795 | 2 |
| #13070753 | 2 |
| #13070699 | 2 |
| C16×D44 | 2 |
| D11×#366 | 2 |
| C4×C11×D16 | 2 |
| #33901 | 11 |