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×#14583335 | C2 | semidirect |
| 3. #19136540 | C2 | semidirect |
| 4. #19136330 | C2 | semidirect |
| 5. #19136216 | C2 | semidirect |
| 6. C43×#3058 | C2 | semidirect |
| 12. #14583699 | C22 | semidirect |
| 16. #14583335 | C22 | semidirect |
| 19. C2×#13063265 | C22 | semidirect |
| 20. #14582708 | C22 | semidirect |
| 21. #14582681 | C22 | semidirect |
| 22. C22×D8×C43 | C22 | semidirect |
| 25. C43×#469 | C22 | semidirect |
| 27. C43×#427 | C22 | semidirect |
| 46. #13063347 | D4 | semidirect |
| 49. C2×Dic172 | D4 | semidirect |
| 53. C2×D344 | D4 | semidirect |
| 199. #3058 | D43 | semidirect |
| 217. C22×D8 | C2×D43 | semidirect |
| 225. #469 | C2×D43 | semidirect |
| 227. #427 | 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×#14583335 | 2 |
| #19136540 | 2 |
| #19136330 | 2 |
| #19136216 | 2 |
| C43×#3058 | 2 |
| #33531 | 43 |