Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D43 | C2 | semidirect |
| 3. #367×D43 | C2 | semidirect |
| 4. #19132783 | C2 | semidirect |
| 5. #19132782 | C2 | semidirect |
| 6. #19132781 | C2 | semidirect |
| 7. C43×#1418 | C2 | semidirect |
| 9. #14583332 | C4 | semidirect |
| 13. #14583328 | C4 | semidirect |
| 14. Q32×D43 | C4 | semidirect |
| 16. D16×D43 | C4 | semidirect |
| 19. #14582733 | C22 | semidirect |
| 22. #14582727 | C22 | semidirect |
| 25. C43×M64 | C22 | semidirect |
| 26. C43×#367 | C22 | semidirect |
| 38. Dic344 | C2×C4 | semidirect |
| 43. D688 | C2×C4 | semidirect |
| 54. Q32×C43 | C2×C4 | semidirect |
| 56. D16×C43 | C2×C4 | semidirect |
| 147. #1418 | D43 | direct (N × H) |
| 153. D43 | #1418 | direct (N × H) |
| 168. M64 | C2×D43 | semidirect |
| 172. #367 | C2×D43 | semidirect |
| 173. C43 | C2×#1418 | semidirect |
| 188. Q32 | C4×D43 | semidirect |
| 195. D16 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D43 | 2 |
| M64×D43 | 2 |
| #367×D43 | 2 |
| #19132783 | 2 |
| #19132782 | 2 |
| #19132781 | 2 |
| C43×#1418 | 2 |
| C2×#1418 | 43 |