Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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×#15668059 | C2 | semidirect |
| 2. #19152396 | C2 | semidirect |
| 3. #19152169 | C2 | semidirect |
| 4. #19151779 | C2 | semidirect |
| 5. #19151769 | C2 | semidirect |
| 6. #19151615 | C2 | semidirect |
| 7. #19151614 | C2 | semidirect |
| 8. C2×#15667930 | C2 | semidirect |
| 9. #575×C89 | C2 | semidirect |
| 21. #15668043 | C22 | semidirect |
| 23. #15668038 | C22 | semidirect |
| 27. #15668010 | C22 | semidirect |
| 28. #15667999 | C22 | semidirect |
| 32. #15667939 | C22 | semidirect |
| 33. #15667938 | C22 | semidirect |
| 34. #15667930 | C22 | semidirect |
| 38. #137×C89 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C89 | C22 | semidirect |
| 186. C89 | #3020 | semidirect |
| 189. #575 | D89 | semidirect |
| 212. #137 | C2×D89 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668059 | 2 |
| #19152396 | 2 |
| #19152169 | 2 |
| #19151779 | 2 |
| #19151769 | 2 |
| #19151615 | 2 |
| #19151614 | 2 |
| C2×#15667930 | 2 |
| #575×C89 | 2 |
| #3020 | 89 |