Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D356 | C2 | semidirect |
| 2. #19151926 | C2 | semidirect |
| 3. #19151909 | C2 | semidirect |
| 4. #19151895 | C2 | semidirect |
| 5. #19151810 | C2 | semidirect |
| 6. #19151748 | C2 | semidirect |
| 8. #19151708 | C2 | semidirect |
| 9. #19151696 | C2 | semidirect |
| 10. #19151655 | C2 | semidirect |
| 11. #529×C89 | C2 | semidirect |
| 22. #15667945 | C22 | semidirect |
| 23. #15667943 | C22 | semidirect |
| 24. C4⋊#10623494 | C22 | semidirect |
| 25. #15667936 | C22 | semidirect |
| 26. #15667933 | C22 | semidirect |
| 31. #15667923 | C22 | semidirect |
| 33. #125×C89 | C22 | semidirect |
| 34. #124×C89 | C22 | semidirect |
| 38. C4×Q8×C89 | C22 | semidirect |
| 40. C4×D4×C89 | C22 | semidirect |
| 141. C89 | #3114 | semidirect |
| 142. #529 | D89 | semidirect |
| 158. #125 | C2×D89 | semidirect |
| 159. #124 | C2×D89 | semidirect |
| 163. C4×Q8 | C2×D89 | semidirect |
| 169. C4×D4 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D356 | 2 |
| #19151926 | 2 |
| #19151909 | 2 |
| #19151895 | 2 |
| #19151810 | 2 |
| #19151748 | 2 |
| #19151731 | 2 |
| #19151708 | 2 |
| #19151696 | 2 |
| #19151655 | 2 |
| #529×C89 | 2 |
| #3114 | 89 |