Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19152109 | C2 | semidirect |
| 2. C2×#15667986 | C2 | semidirect |
| 3. #19151934 | C2 | semidirect |
| 4. #19151923 | C2 | semidirect |
| 5. #19151917 | C2 | semidirect |
| 6. #19151834 | C2 | semidirect |
| 7. #19151827 | C2 | semidirect |
| 8. #19151751 | C2 | semidirect |
| 9. #19151745 | C2 | semidirect |
| 10. #19151734 | C2 | semidirect |
| 11. C2×C22⋊C8×C89 | C2 | semidirect |
| 12. C2×#13083574 | C22 | semidirect |
| 15. C2×#13083563 | C22 | semidirect |
| 16. C2×D712 | C22 | semidirect |
| 19. #15667991 | C22 | semidirect |
| 25. #15667986 | C22 | semidirect |
| 29. #15667971 | C22 | semidirect |
| 32. #15667946 | C22 | semidirect |
| 33. #15667944 | C22 | semidirect |
| 34. #15667937 | C22 | semidirect |
| 35. #15667934 | C22 | semidirect |
| 36. #15667934 | C22 | semidirect |
| 37. #15667934 | C22 | semidirect |
| 39. C22×C8×C89 | C22 | semidirect |
| 42. C22⋊C8×C89 | C22 | semidirect |
| 159. C89 | #3188 | semidirect |
| 170. C2×C22⋊C8 | D89 | semidirect |
| 177. C22×C8 | C2×D89 | semidirect |
| 201. C22⋊C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152109 | 2 |
| C2×#15667986 | 2 |
| #19151934 | 2 |
| #19151923 | 2 |
| #19151917 | 2 |
| #19151834 | 2 |
| #19151827 | 2 |
| #19151751 | 2 |
| #19151745 | 2 |
| #19151734 | 2 |
| C2×C22⋊C8×C89 | 2 |
| #3188 | 89 |