Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15668040 | C2 | semidirect |
| 2. #19152148 | C2 | semidirect |
| 3. C2×C4×D356 | C2 | semidirect |
| 4. #19151814 | C2 | semidirect |
| 5. #19151804 | C2 | semidirect |
| 6. #19151794 | C2 | semidirect |
| 7. #19151600 | C2 | semidirect |
| 8. #423×C89 | C2 | semidirect |
| 15. #15668012 | C22 | semidirect |
| 16. #15668009 | C22 | semidirect |
| 17. #15668000 | C22 | semidirect |
| 28. #15667937 | C22 | semidirect |
| 29. #15667934 | C22 | semidirect |
| 32. C4⋊C8×C89 | C22 | semidirect |
| 33. C4⋊C8×C89 | C22 | semidirect |
| 42. C2×D356 | D4 | semidirect |
| 118. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 130. C89 | #3036 | semidirect |
| 137. #423 | D89 | semidirect |
| 160. C4⋊C8 | C2×D89 | semidirect |
| 161. C4⋊C8 | C2×D89 | semidirect |
| 250. C4 | #15668040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668040 | 2 |
| #19152148 | 2 |
| C2×C4×D356 | 2 |
| #19151814 | 2 |
| #19151804 | 2 |
| #19151794 | 2 |
| #19151600 | 2 |
| #423×C89 | 2 |
| #3036 | 89 |