Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
5838 conjugacy classes of subgroups; only the 1339 normal subgroups are shown.
This group has 5838 conjugacy classes of subgroups — too many to draw. Only its 1339 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. C23×Dic11⋊C4 | C2 | semidirect |
| 3. C2×#10622289 | C2 | direct (N × H) |
| 4. C22×C11×#95 | C2 | semidirect |
| 11. C22×Dic11⋊C4 | C22 | semidirect |
| 12. C2×C11×#95 | C22 | semidirect |
| 13. #10622289 | C22 | direct (N × H) |
| 30. C2×Dic11⋊C4 | C23 | semidirect |
| 31. C11×#95 | C23 | semidirect |
| 59. C22×#95 | D11 | semidirect |
| 90. C2×#95 | C2×D11 | semidirect |
| 91. C22×C11 | #396 | semidirect |
| 121. #95 | C22×D11 | semidirect |
| 122. C2×C11 | C2×#396 | semidirect |
| 150. C11 | C22×#396 | semidirect |
| 177. C22 | #10622289 | direct (N × H) |
| 187. C2 | C2×#10622289 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic11⋊C4 | 2 |
| C23×(C2×D11)⋊C4 | 2 |
| C2×#10622289 | 2 |
| C22×C11×#95 | 2 |
| C22×#396 | 11 |