Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
670 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×D176 | C2 | semidirect |
| 2. C2×#10622728 | C2 | semidirect |
| 3. C2×#10622147 | C2 | semidirect |
| 4. #13066708 | C2 | semidirect |
| 5. C2×C11×C22⋊C16 | C2 | semidirect |
| 37. C2×D88 | D4 | semidirect |
| 41. C2×C11×C16 | D4 | semidirect |
| 44. #66882 | D4 | semidirect |
| 86. C2×C22⋊C16 | D11 | semidirect |
| 92. C23×C11 | D16 | semidirect |
| 180. C2×C16 | C22⋊D11 | semidirect |
| 227. C11 | #13304 | semidirect |
| 239. C23 | D176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C2×#10622728 | 2 |
| C2×#10622147 | 2 |
| #13066708 | 2 |
| C2×C11×C22⋊C16 | 2 |
| #13304 | 11 |