Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×D344 | C2 | semidirect |
| 2. C2×#14583337 | C2 | semidirect |
| 3. #19144176 | C2 | semidirect |
| 4. #19136526 | C2 | semidirect |
| 5. #19136509 | C2 | semidirect |
| 6. #19136312 | C2 | semidirect |
| 7. C43×#2112 | C2 | semidirect |
| 9. C2×#13063347 | C22 | semidirect |
| 17. C2×#13063270 | C22 | semidirect |
| 18. C2×D688 | C22 | semidirect |
| 19. #14583140 | C22 | semidirect |
| 20. #14583135 | C22 | semidirect |
| 22. #14582937 | C22 | semidirect |
| 24. #14582701 | C22 | semidirect |
| 26. C2×M32×C43 | C22 | semidirect |
| 27. C43×C22⋊C16 | C22 | semidirect |
| 37. C2×Dic172 | C23 | semidirect |
| 45. C2×D344 | D4 | semidirect |
| 47. C2×D344 | C23 | semidirect |
| 56. #13063259 | C23 | semidirect |
| 67. C2×C16×C43 | C23 | semidirect |
| 159. C22×C43 | #509 | semidirect |
| 179. #2112 | D43 | semidirect |
| 198. C2×M32 | C2×D43 | semidirect |
| 205. C22⋊C16 | C2×D43 | semidirect |
| 206. C43 | #33517 | semidirect |
| 242. C2×C16 | C22×D43 | semidirect |
| 343. C22 | #14583337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D344 | 2 |
| C2×#14583337 | 2 |
| #19144176 | 2 |
| #19136526 | 2 |
| #19136509 | 2 |
| #19136312 | 2 |
| C43×#2112 | 2 |
| #33517 | 43 |