Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
344 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19136285 | C2 | semidirect |
| 3. #19136263 | C2 | semidirect |
| 4. #19132770 | C2 | semidirect |
| 5. #19132753 | C2 | semidirect |
| 6. #19132751 | C2 | semidirect |
| 7. C43×#1414 | C2 | semidirect |
| 8. #14583505 | C4 | semidirect |
| 11. #14583276 | C4 | semidirect |
| 12. #14583265 | C4 | semidirect |
| 17. #14582958 | C4 | semidirect |
| 35. #13063322 | C2×C4 | semidirect |
| 54. #13063236 | C2×C4 | semidirect |
| 55. #125×C43 | C2×C4 | semidirect |
| 61. C4×C8×C43 | C2×C4 | semidirect |
| 167. #1414 | D43 | semidirect |
| 196. C43 | #13605 | semidirect |
| 207. #125 | C4×D43 | semidirect |
| 231. C4×C8 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145648 | 2 |
| #19136285 | 2 |
| #19136263 | 2 |
| #19132770 | 2 |
| #19132753 | 2 |
| #19132751 | 2 |
| C43×#1414 | 2 |
| #13605 | 43 |