Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13083563 | C2 | semidirect |
| 2. #19152169 | C2 | semidirect |
| 4. #19151844 | C2 | semidirect |
| 5. #19151827 | C2 | semidirect |
| 6. #19151636 | C2 | semidirect |
| 7. #19151608 | C2 | semidirect |
| 8. #19151604 | C2 | semidirect |
| 9. C2×#131×C89 | C2 | semidirect |
| 20. #15667991 | C22 | semidirect |
| 25. #15667946 | C22 | semidirect |
| 26. #15667944 | C22 | semidirect |
| 27. #15667937 | C22 | semidirect |
| 32. C2×M16×C89 | C22 | semidirect |
| 34. C22×C8×C89 | C22 | semidirect |
| 67. C2×C8×C89 | D4 | semidirect |
| 121. C89 | #3057 | semidirect |
| 123. C2×#131 | D89 | semidirect |
| 139. C2×M16 | C2×D89 | semidirect |
| 141. C22×C8 | C2×D89 | semidirect |
| 179. C2×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083563 | 2 |
| #19152169 | 2 |
| #19152162 | 2 |
| #19151844 | 2 |
| #19151827 | 2 |
| #19151636 | 2 |
| #19151608 | 2 |
| #19151604 | 2 |
| C2×#131×C89 | 2 |
| #3057 | 89 |