Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #19147732 | C2 | semidirect |
| 2. #19146394 | C2 | semidirect |
| 3. #19136712 | C2 | semidirect |
| 4. #19136668 | C2 | semidirect |
| 5. #19136551 | C2 | semidirect |
| 6. #19136477 | C2 | semidirect |
| 7. #19136433 | C2 | semidirect |
| 8. C43×#2246 | C2 | semidirect |
| 10. #14583700 | C22 | semidirect |
| 11. #14583335 | C22 | semidirect |
| 16. #14583315 | C22 | semidirect |
| 18. #14583166 | C22 | semidirect |
| 21. #14583017 | C22 | semidirect |
| 22. #14582729 | C22 | semidirect |
| 23. #14582720 | C22 | semidirect |
| 24. #14582712 | C22 | semidirect |
| 25. #14582707 | C22 | semidirect |
| 26. #14582682 | C22 | semidirect |
| 27. C2×D16×C43 | C22 | semidirect |
| 28. C2×D16×C43 | C22 | semidirect |
| 29. C43×#493 | C22 | semidirect |
| 30. C4×C16×C43 | C22 | semidirect |
| 44. Dic344 | D4 | semidirect |
| 45. #13063270 | D4 | semidirect |
| 47. D688 | D4 | semidirect |
| 140. #2246 | D43 | semidirect |
| 158. C2×D16 | C2×D43 | semidirect |
| 159. C2×D16 | C2×D43 | semidirect |
| 161. #493 | C2×D43 | semidirect |
| 172. C4×C16 | C2×D43 | semidirect |
| 173. C43 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147732 | 2 |
| #19146394 | 2 |
| #19136712 | 2 |
| #19136668 | 2 |
| #19136551 | 2 |
| #19136477 | 2 |
| #19136433 | 2 |
| C43×#2246 | 2 |
| #33858 | 43 |