Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
14334 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C24×Dic22 | C2 | semidirect |
| 2. C22×#66989 | C2 | direct (N × H) |
| 3. C23×C22⋊Dic11 | C2 | semidirect |
| 4. C23×C4×Dic11 | C2 | semidirect |
| 13. C23×Dic22 | C22 | semidirect |
| 14. C22×C22⋊Dic11 | C22 | semidirect |
| 15. C2×#66989 | C22 | direct (N × H) |
| 16. C22×C4×Dic11 | C22 | semidirect |
| 30. C22×Dic22 | C23 | semidirect |
| 31. C2×C22⋊Dic11 | C23 | semidirect |
| 32. #66989 | C23 | direct (N × H) |
| 33. C2×C4×Dic11 | C23 | semidirect |
| 51. C2×Dic22 | C24 | semidirect |
| 52. C22⋊Dic11 | C24 | semidirect |
| 53. C4×Dic11 | C24 | semidirect |
| 62. C23×C11 | #124 | semidirect |
| 89. C22×C11 | C2×#124 | semidirect |
| 114. C2×C11 | C22×#124 | semidirect |
| 136. C11 | C23×#124 | semidirect |
| 140. C23 | #66989 | direct (N × H) |
| 156. C22 | C2×#66989 | direct (N × H) |
| 164. C2 | C22×#66989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic22 | 2 |
| C22×#66989 | 2 |
| C23×C22⋊Dic11 | 2 |
| C23×C4×Dic11 | 2 |
| C24×D4×C11 | 2 |
| C23×#124 | 11 |