Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
7134 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1771 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×#4318 | C2 | semidirect |
| 2. C22×#66897 | C2 | direct (N × H) |
| 11. C22×#4318 | C22 | semidirect |
| 13. C2×#66897 | C22 | direct (N × H) |
| 30. C2×#4318 | C23 | semidirect |
| 32. #66897 | C23 | direct (N × H) |
| 57. #4318 | C24 | semidirect |
| 69. C23×C11 | #100 | semidirect |
| 99. C22×C11 | C2×#100 | semidirect |
| 127. C2×C11 | C22×#100 | semidirect |
| 154. C11 | C23×#100 | semidirect |
| 162. C23 | #66897 | direct (N × H) |
| 182. C22 | C2×#66897 | direct (N × H) |
| 191. C2 | C22×#66897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#4318 | 2 |
| C22×#66897 | 2 |
| C24×D4×C11 | 2 |
| C23×#100 | 11 |