Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #19149369 | C2 | semidirect |
| 2. C2×#14583337 | C2 | semidirect |
| 3. #19144243 | C2 | semidirect |
| 4. #19136543 | C2 | semidirect |
| 5. #19136332 | C2 | semidirect |
| 6. C43×#2115 | C2 | semidirect |
| 12. #14583699 | C22 | semidirect |
| 15. C22×D344 | C22 | semidirect |
| 18. #14583337 | C22 | semidirect |
| 21. #14583152 | C22 | semidirect |
| 23. #14582937 | C22 | semidirect |
| 25. #14582710 | C22 | semidirect |
| 27. C2×M32×C43 | C22 | semidirect |
| 28. C43×#349 | C22 | semidirect |
| 47. #13063347 | D4 | semidirect |
| 50. C2×Dic172 | D4 | semidirect |
| 57. C2×D344 | D4 | semidirect |
| 202. #2115 | D43 | semidirect |
| 224. C2×M32 | C2×D43 | semidirect |
| 230. #349 | C2×D43 | semidirect |
| 231. C43 | #33531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149369 | 2 |
| C2×#14583337 | 2 |
| #19144243 | 2 |
| #19136543 | 2 |
| #19136332 | 2 |
| C43×#2115 | 2 |
| #33531 | 43 |