Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19152134 | C2 | semidirect |
| 2. C2×#15668001 | C2 | semidirect |
| 3. #19151983 | C2 | semidirect |
| 4. #19151954 | C2 | semidirect |
| 5. #19151822 | C2 | semidirect |
| 6. #19151816 | C2 | semidirect |
| 7. #19151748 | C2 | semidirect |
| 8. #19151737 | C2 | semidirect |
| 10. #19151648 | C2 | semidirect |
| 11. #451×C89 | C2 | semidirect |
| 14. C2×#13083561 | C22 | semidirect |
| 17. #15668003 | C22 | semidirect |
| 22. #15668001 | C22 | semidirect |
| 25. Q8×Dic89 | C22 | semidirect |
| 26. #15667974 | C22 | semidirect |
| 32. #15667941 | C22 | semidirect |
| 33. #15667936 | C22 | semidirect |
| 37. C8×Dic89 | C22 | semidirect |
| 39. C2×Q16×C89 | C22 | semidirect |
| 41. #103×C89 | C22 | semidirect |
| 144. C89 | #3211 | semidirect |
| 151. #451 | D89 | semidirect |
| 158. C2×Q16 | C2×D89 | semidirect |
| 181. #103 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152134 | 2 |
| C2×#15668001 | 2 |
| #19151983 | 2 |
| #19151954 | 2 |
| #19151822 | 2 |
| #19151816 | 2 |
| #19151748 | 2 |
| #19151737 | 2 |
| #19151734 | 2 |
| #19151648 | 2 |
| #451×C89 | 2 |
| #3211 | 89 |