Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19152313 | C2 | semidirect |
| 2. D4×D356 | C2 | semidirect |
| 3. #19151945 | C2 | semidirect |
| 4. #19151923 | C2 | semidirect |
| 5. #19151889 | C2 | semidirect |
| 6. #19151851 | C2 | semidirect |
| 7. #19151794 | C2 | semidirect |
| 8. #19151734 | C2 | semidirect |
| 9. C4×D712 | C2 | semidirect |
| 10. #19151604 | C2 | semidirect |
| 11. #436×C89 | C2 | semidirect |
| 15. C2×D712 | C22 | semidirect |
| 16. #15668012 | C22 | semidirect |
| 21. #15667986 | C22 | semidirect |
| 25. C4×D356 | C22 | semidirect |
| 26. #15667971 | C22 | semidirect |
| 28. #15667946 | C22 | semidirect |
| 29. #15667944 | C22 | semidirect |
| 32. #15667934 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 34. #15667934 | C22 | semidirect |
| 35. #15667934 | C22 | semidirect |
| 36. C2×M16×C89 | C22 | semidirect |
| 38. C4⋊C8×C89 | C22 | semidirect |
| 39. C22⋊C8×C89 | C22 | semidirect |
| 40. C4×C8×C89 | C22 | semidirect |
| 141. C89 | #3325 | semidirect |
| 151. #436 | D89 | semidirect |
| 157. C2×M16 | C2×D89 | semidirect |
| 173. C4⋊C8 | C2×D89 | semidirect |
| 180. C22⋊C8 | C2×D89 | semidirect |
| 181. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152313 | 2 |
| D4×D356 | 2 |
| #19151945 | 2 |
| #19151923 | 2 |
| #19151889 | 2 |
| #19151851 | 2 |
| #19151794 | 2 |
| #19151734 | 2 |
| C4×D712 | 2 |
| #19151604 | 2 |
| #436×C89 | 2 |
| #3325 | 89 |