Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668045 | C2 | semidirect |
| 3. C2×#15668000 | C2 | semidirect |
| 4. C4×#13083574 | C2 | semidirect |
| 5. #19151821 | C2 | semidirect |
| 6. #19151814 | C2 | semidirect |
| 7. #19151608 | C2 | semidirect |
| 8. #19151604 | C2 | semidirect |
| 9. #423×C89 | C2 | semidirect |
| 15. C2×Dic356 | C22 | semidirect |
| 17. C2×#13083563 | C22 | semidirect |
| 22. C4×Dic178 | C22 | semidirect |
| 23. C4×D356 | C22 | semidirect |
| 29. #15667937 | C22 | semidirect |
| 34. C4⋊C8×C89 | C22 | semidirect |
| 126. C89 | #3040 | semidirect |
| 133. #423 | D89 | semidirect |
| 158. C4⋊C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668045 | 2 |
| C2×#15668040 | 2 |
| C2×#15668000 | 2 |
| C4×#13083574 | 2 |
| #19151821 | 2 |
| #19151814 | 2 |
| #19151608 | 2 |
| #19151604 | 2 |
| #423×C89 | 2 |
| #3040 | 89 |