Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152210 | C2 | semidirect |
| 3. #19151992 | C2 | semidirect |
| 4. #19151971 | C2 | semidirect |
| 5. #19151963 | C2 | semidirect |
| 6. #19151953 | C2 | semidirect |
| 7. #19151821 | C2 | semidirect |
| 8. #19151799 | C2 | semidirect |
| 9. #19151762 | C2 | semidirect |
| 10. #19151751 | C2 | semidirect |
| 11. #433×C89 | C2 | semidirect |
| 14. C2×Dic356 | C22 | semidirect |
| 17. C2×#13083563 | C22 | semidirect |
| 18. #15668012 | C22 | semidirect |
| 22. #15668004 | C22 | semidirect |
| 29. C4×Dic178 | C22 | semidirect |
| 30. #15667937 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 35. C4⋊C8×C89 | C22 | semidirect |
| 37. #97×C89 | C22 | semidirect |
| 38. C4×C8×C89 | C22 | semidirect |
| 123. C89 | #3222 | semidirect |
| 134. #433 | D89 | semidirect |
| 154. C4⋊C8 | C2×D89 | semidirect |
| 160. #97 | C2×D89 | semidirect |
| 161. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152210 | 2 |
| #19152167 | 2 |
| #19151992 | 2 |
| #19151971 | 2 |
| #19151963 | 2 |
| #19151953 | 2 |
| #19151821 | 2 |
| #19151799 | 2 |
| #19151762 | 2 |
| #19151751 | 2 |
| #433×C89 | 2 |
| #3222 | 89 |