Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #13079148 | C2 | semidirect |
| 4. #13066722 | C2 | semidirect |
| 5. #13066717 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 30. C2×C11×Q16 | Q8 | semidirect |
| 32. C2×C11×D8 | Q8 | semidirect |
| 181. C2×Q16 | Dic22 | semidirect |
| 183. C2×D8 | Dic22 | semidirect |
| 262. C11 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079148 | 2 |
| C2×#10622204 | 2 |
| #13069515 | 2 |
| #13066722 | 2 |
| #13066717 | 2 |
| #13066701 | 2 |
| C11×#2145 | 2 |
| #13374 | 11 |