Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1102 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1102 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. #19147731 | C2 | semidirect |
| 3. #19144257 | C2 | semidirect |
| 4. #19136548 | C2 | semidirect |
| 5. #19136543 | C2 | semidirect |
| 6. C2×#14582710 | C2 | semidirect |
| 7. C43×#2115 | C2 | semidirect |
| 16. C2×#13063347 | C22 | semidirect |
| 19. #14583342 | C22 | semidirect |
| 21. #14583337 | C22 | semidirect |
| 23. #14583157 | C22 | semidirect |
| 24. #14583152 | C22 | semidirect |
| 26. C2×#13063257 | C22 | semidirect |
| 28. #14582710 | C22 | semidirect |
| 30. C2×M32×C43 | C22 | semidirect |
| 31. C43×#349 | C22 | semidirect |
| 52. #13063347 | D4 | semidirect |
| 55. C2×Dic172 | D4 | semidirect |
| 61. C2×D344 | D4 | semidirect |
| 219. #2115 | D43 | semidirect |
| 242. C2×M32 | C2×D43 | semidirect |
| 249. #349 | C2×D43 | semidirect |
| 250. C43 | #33533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149369 | 2 |
| #19147731 | 2 |
| #19144257 | 2 |
| #19136548 | 2 |
| #19136543 | 2 |
| C2×#14582710 | 2 |
| C43×#2115 | 2 |
| #33533 | 43 |