Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
712 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#14583336 | C2 | semidirect |
| 2. #19146279 | C2 | semidirect |
| 3. #19136705 | C2 | semidirect |
| 4. #19136647 | C2 | semidirect |
| 5. #19136534 | C2 | semidirect |
| 6. #19136505 | C2 | semidirect |
| 7. C4×D688 | C2 | semidirect |
| 8. #19136428 | C2 | semidirect |
| 9. C43×#2249 | C2 | semidirect |
| 11. C2×D8×D43 | C22 | semidirect |
| 14. C2×#13063268 | C22 | semidirect |
| 17. C2×#13063264 | C22 | semidirect |
| 18. #14583137 | C22 | semidirect |
| 23. C4×D344 | C22 | semidirect |
| 25. #14582725 | C22 | semidirect |
| 26. C4⋊(C43⋊C16) | C22 | semidirect |
| 27. #14582703 | C22 | semidirect |
| 28. #14582701 | C22 | semidirect |
| 29. #14582700 | C22 | semidirect |
| 30. (C2×D43)⋊C16 | C22 | semidirect |
| 31. C2×Q32×C43 | C22 | semidirect |
| 32. C2×SD32×C43 | C22 | semidirect |
| 34. C43×#495 | C22 | semidirect |
| 35. C4×C16×C43 | C22 | semidirect |
| 55. D688 | D4 | semidirect |
| 168. #2249 | D43 | semidirect |
| 185. C2×Q32 | C2×D43 | semidirect |
| 187. C2×SD32 | C2×D43 | semidirect |
| 192. #495 | C2×D43 | semidirect |
| 206. C4×C16 | C2×D43 | semidirect |
| 207. C43 | #33839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583336 | 2 |
| #19146279 | 2 |
| #19136705 | 2 |
| #19136647 | 2 |
| #19136534 | 2 |
| #19136505 | 2 |
| C4×D688 | 2 |
| #19136428 | 2 |
| C43×#2249 | 2 |
| #33839 | 43 |