Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #13079144 | C2 | semidirect |
| 5. #13066717 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 7. C11×#1386 | C2 | semidirect |
| 33. C2×Dic44 | Q8 | semidirect |
| 38. C2×D88 | Q8 | semidirect |
| 111. #1386 | D11 | semidirect |
| 262. C11 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079144 | 2 |
| #13070353 | 2 |
| C2×#10622126 | 2 |
| #13069512 | 2 |
| #13066717 | 2 |
| #13066701 | 2 |
| C11×#1386 | 2 |
| #13374 | 11 |