Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×#15667988 | C2 | semidirect |
| 3. #19151938 | C2 | semidirect |
| 4. #19151926 | C2 | semidirect |
| 5. #19151912 | C2 | semidirect |
| 6. #19151836 | C2 | semidirect |
| 7. #19151830 | C2 | semidirect |
| 8. #19151759 | C2 | semidirect |
| 9. #19151737 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #451×C89 | C2 | semidirect |
| 14. C2×#13083561 | C22 | semidirect |
| 31. #15667946 | C22 | semidirect |
| 32. #15667943 | C22 | semidirect |
| 33. #15667936 | C22 | semidirect |
| 34. #15667936 | C22 | semidirect |
| 35. #15667934 | C22 | semidirect |
| 39. C2×Q16×C89 | C22 | semidirect |
| 41. #103×C89 | C22 | semidirect |
| 150. C89 | #3190 | semidirect |
| 159. #451 | D89 | semidirect |
| 165. C2×Q16 | C2×D89 | semidirect |
| 188. #103 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152111 | 2 |
| C2×#15667988 | 2 |
| #19151938 | 2 |
| #19151926 | 2 |
| #19151912 | 2 |
| #19151836 | 2 |
| #19151830 | 2 |
| #19151759 | 2 |
| #19151737 | 2 |
| C22⋊C8×D89 | 2 |
| #451×C89 | 2 |
| #3190 | 89 |