Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19152132 | C2 | semidirect |
| 2. C2×#15668000 | C2 | semidirect |
| 3. #19151982 | C2 | semidirect |
| 4. #19151953 | C2 | semidirect |
| 5. #19151821 | C2 | semidirect |
| 6. #19151814 | C2 | semidirect |
| 7. #19151756 | C2 | semidirect |
| 8. #19151751 | C2 | semidirect |
| 9. #19151739 | C2 | semidirect |
| 11. #431×C89 | C2 | semidirect |
| 14. C2×Dic356 | C22 | semidirect |
| 16. C2×#13083563 | C22 | semidirect |
| 19. #15668004 | C22 | semidirect |
| 24. #15668000 | C22 | semidirect |
| 28. C4×Dic178 | C22 | semidirect |
| 29. C4×D356 | C22 | semidirect |
| 34. #15667937 | C22 | semidirect |
| 35. #15667937 | C22 | semidirect |
| 39. C4⋊C8×C89 | C22 | semidirect |
| 42. C4×C8×C89 | C22 | semidirect |
| 144. C89 | #3211 | semidirect |
| 155. #431 | D89 | semidirect |
| 179. C4⋊C8 | C2×D89 | semidirect |
| 186. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152132 | 2 |
| C2×#15668000 | 2 |
| #19151982 | 2 |
| #19151953 | 2 |
| #19151821 | 2 |
| #19151814 | 2 |
| #19151756 | 2 |
| #19151751 | 2 |
| #19151739 | 2 |
| #19151734 | 2 |
| #431×C89 | 2 |
| #3211 | 89 |