Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
12190 conjugacy classes of subgroups; only the 4939 normal subgroups are shown.
This group has 12190 conjugacy classes of subgroups — too many to draw. Only its 4939 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×#66997 | C2 | direct (N × H) |
| 14. C2×#66997 | C22 | direct (N × H) |
| 25. C23×Dic11 | Q8 | semidirect |
| 30. #66997 | C23 | direct (N × H) |
| 44. C22×Dic11 | C2×Q8 | semidirect |
| 56. C23×C11 | C4⋊Q8 | semidirect |
| 66. C2×Dic11 | C22×Q8 | semidirect |
| 81. C22×C11 | C2×C4⋊Q8 | semidirect |
| 88. Dic11 | C23×Q8 | semidirect |
| 105. C2×C11 | C22×C4⋊Q8 | semidirect |
| 125. C11 | C23×C4⋊Q8 | semidirect |
| 126. C23 | #66997 | direct (N × H) |
| 140. C22 | C2×#66997 | direct (N × H) |
| 148. C2 | C22×#66997 | 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×#66997 | 2 |
| C23×Dic11⋊C4 | 2 |
| C23×C4×Dic11 | 2 |
| C24×Q8×C11 | 2 |
| C23×C4⋊Q8 | 11 |