Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#15668043 | C2 | semidirect |
| 2. C2×M16×D89 | C2 | semidirect |
| 4. C2×#15667988 | C2 | semidirect |
| 5. #19151855 | C2 | semidirect |
| 6. #19151847 | C2 | semidirect |
| 7. #19151838 | C2 | semidirect |
| 8. #19151830 | C2 | semidirect |
| 9. #19151641 | C2 | semidirect |
| 10. #19151600 | C2 | semidirect |
| 11. #419×C89 | C2 | semidirect |
| 15. C2×#13083564 | C22 | semidirect |
| 16. C2×#13083561 | C22 | semidirect |
| 36. #15667945 | C22 | semidirect |
| 37. #15667943 | C22 | semidirect |
| 38. #15667937 | C22 | semidirect |
| 39. #15667934 | C22 | semidirect |
| 43. #103×C89 | C22 | semidirect |
| 44. #103×C89 | C22 | semidirect |
| 64. #13083558 | D4 | semidirect |
| 145. C2×D89 | #137 | semidirect |
| 164. C89 | #3056 | semidirect |
| 174. #419 | D89 | semidirect |
| 206. #103 | C2×D89 | semidirect |
| 207. #103 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668043 | 2 |
| C2×M16×D89 | 2 |
| #19152110 | 2 |
| C2×#15667988 | 2 |
| #19151855 | 2 |
| #19151847 | 2 |
| #19151838 | 2 |
| #19151830 | 2 |
| #19151641 | 2 |
| #19151600 | 2 |
| #419×C89 | 2 |
| #3056 | 89 |