Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
15150 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 15150 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 |
|---|---|---|
| 2. C22×#66982 | C2 | direct (N × H) |
| 3. C23×Dic11⋊C4 | C2 | semidirect |
| 4. C23×C22⋊Dic11 | C2 | semidirect |
| 5. C23×(C2×D11)⋊C4 | C2 | semidirect |
| 6. C25×C4×C11 | C2 | semidirect |
| 11. C24×C4×C11 | C22 | semidirect |
| 16. C22×C22⋊Dic11 | C22 | semidirect |
| 17. C2×#66982 | C22 | direct (N × H) |
| 18. C22×(C2×D11)⋊C4 | C22 | semidirect |
| 19. C22×Dic11⋊C4 | C22 | semidirect |
| 30. C23×C4×C11 | C23 | semidirect |
| 37. C2×C22⋊Dic11 | C23 | semidirect |
| 38. #66982 | C23 | direct (N × H) |
| 39. C2×(C2×D11)⋊C4 | C23 | semidirect |
| 40. C2×Dic11⋊C4 | C23 | semidirect |
| 56. C22×C4×C11 | C24 | semidirect |
| 63. C22⋊Dic11 | C24 | semidirect |
| 64. (C2×D11)⋊C4 | C24 | semidirect |
| 65. Dic11⋊C4 | C24 | semidirect |
| 67. C25×C4 | D11 | semidirect |
| 74. C23×C11 | #123 | semidirect |
| 100. C24×C4 | C2×D11 | semidirect |
| 107. C22×C11 | C2×#123 | semidirect |
| 134. C23×C4 | C22×D11 | semidirect |
| 140. C2×C11 | C22×#123 | semidirect |
| 164. C22×C4 | C23×D11 | semidirect |
| 168. C11 | C23×#123 | semidirect |
| 175. C23 | #66982 | direct (N × H) |
| 194. C22 | C2×#66982 | direct (N × H) |
| 204. C2 | C22×#66982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C22⋊D11 | 2 |
| C22×#66982 | 2 |
| C23×Dic11⋊C4 | 2 |
| C23×C22⋊Dic11 | 2 |
| C23×(C2×D11)⋊C4 | 2 |
| C25×C4×C11 | 2 |
| C23×#123 | 11 |