Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #13068234 | C2 | semidirect |
| 4. #13066673 | C2 | semidirect |
| 5. C11×#1370 | C2 | semidirect |
| 51. D88 | Q16 | semidirect |
| 57. #1370 | D11 | semidirect |
| 139. C11 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070764 | 2 |
| #13068234 | 2 |
| C8×D88 | 2 |
| #13066673 | 2 |
| C11×#1370 | 2 |
| #12447 | 11 |