Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×D176 | C2 | semidirect |
| 2. C22×#66862 | C2 | semidirect |
| 3. C2×#10622496 | C2 | semidirect |
| 4. #13070720 | C2 | direct (N × H) |
| 5. C2×#10622129 | C2 | semidirect |
| 6. C2×C11×#367 | C2 | semidirect |
| 15. C2×D176 | C22 | semidirect |
| 17. C2×#66862 | C22 | semidirect |
| 19. #10622496 | C22 | semidirect |
| 20. C11×#367 | C22 | semidirect |
| 21. #10622129 | C22 | semidirect |
| 39. C2×C11×C16 | D4 | semidirect |
| 79. C11×C16 | C2×D4 | semidirect |
| 85. C2×#367 | D11 | semidirect |
| 127. #367 | C2×D11 | semidirect |
| 165. C2×C16 | D44 | semidirect |
| 170. C2×C11 | #2218 | semidirect |
| 206. C16 | C2×D44 | semidirect |
| 207. C11 | C2×#2218 | semidirect |
| 252. C2 | #13070720 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| C22×#66862 | 2 |
| C2×#10622496 | 2 |
| #13070720 | 2 |
| C2×#10622129 | 2 |
| C2×C11×#367 | 2 |
| C2×#2218 | 11 |