Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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. #19152132 | C2 | semidirect |
| 2. C2×C4×D356 | C2 | semidirect |
| 3. #19151934 | C2 | semidirect |
| 4. #19151917 | C2 | semidirect |
| 5. #19151899 | C2 | semidirect |
| 6. #19151814 | C2 | semidirect |
| 7. #19151751 | C2 | semidirect |
| 9. C4×#13083563 | C2 | semidirect |
| 10. C4×D712 | C2 | semidirect |
| 11. #431×C89 | C2 | semidirect |
| 17. #15668004 | C22 | semidirect |
| 18. #15668000 | C22 | semidirect |
| 22. C4×Dic178 | C22 | semidirect |
| 27. C4×D356 | C22 | semidirect |
| 32. #15667946 | C22 | semidirect |
| 33. #15667944 | C22 | semidirect |
| 34. #15667937 | C22 | semidirect |
| 37. #15667934 | C22 | semidirect |
| 39. C4⋊C8×C89 | C22 | semidirect |
| 42. C4×C8×C89 | C22 | semidirect |
| 141. C89 | #3105 | semidirect |
| 152. #431 | D89 | semidirect |
| 176. C4⋊C8 | C2×D89 | semidirect |
| 183. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152132 | 2 |
| C2×C4×D356 | 2 |
| #19151934 | 2 |
| #19151917 | 2 |
| #19151899 | 2 |
| #19151814 | 2 |
| #19151751 | 2 |
| #19151734 | 2 |
| C4×#13083563 | 2 |
| C4×D712 | 2 |
| #431×C89 | 2 |
| #3105 | 89 |