Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15668033 | C2 | semidirect |
| 2. #19152149 | C2 | semidirect |
| 3. C4×#13083573 | C2 | semidirect |
| 4. #19151823 | C2 | semidirect |
| 5. #19151815 | C2 | semidirect |
| 6. #19151805 | C2 | semidirect |
| 7. #19151799 | C2 | semidirect |
| 8. #19151793 | C2 | semidirect |
| 9. C4⋊C8×D89 | C2 | semidirect |
| 10. #19151593 | C2 | semidirect |
| 11. #461×C89 | C2 | semidirect |
| 47. #13083573 | D4 | semidirect |
| 136. C4×C89 | #135 | semidirect |
| 151. C89 | #3035 | semidirect |
| 158. #461 | D89 | semidirect |
| 292. C4 | #15668033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668033 | 2 |
| #19152149 | 2 |
| C4×#13083573 | 2 |
| #19151823 | 2 |
| #19151815 | 2 |
| #19151805 | 2 |
| #19151799 | 2 |
| #19151793 | 2 |
| C4⋊C8×D89 | 2 |
| #19151593 | 2 |
| #461×C89 | 2 |
| #3035 | 89 |