Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#15668037 | C2 | semidirect |
| 3. #19152144 | C2 | semidirect |
| 4. C2×#15667974 | C2 | semidirect |
| 5. #19151816 | C2 | semidirect |
| 6. #19151812 | C2 | semidirect |
| 7. #19151802 | C2 | semidirect |
| 8. #19151792 | C2 | semidirect |
| 9. #19151621 | C2 | semidirect |
| 10. #19151597 | C2 | semidirect |
| 11. #417×C89 | C2 | semidirect |
| 22. #15668010 | C22 | semidirect |
| 23. #15668008 | C22 | semidirect |
| 24. #15668001 | C22 | semidirect |
| 25. #15667999 | C22 | semidirect |
| 36. #15667941 | C22 | semidirect |
| 37. #15667941 | C22 | semidirect |
| 38. #15667935 | C22 | semidirect |
| 39. #15667932 | C22 | semidirect |
| 43. #103×C89 | C22 | semidirect |
| 44. #102×C89 | C22 | semidirect |
| 51. C2×D356 | D4 | semidirect |
| 158. Dic89 | AGL(1,ℤ/8) | semidirect |
| 167. C89 | #3036 | semidirect |
| 178. #417 | D89 | semidirect |
| 209. #103 | C2×D89 | semidirect |
| 211. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668040 | 2 |
| C2×#15668037 | 2 |
| #19152144 | 2 |
| C2×#15667974 | 2 |
| #19151816 | 2 |
| #19151812 | 2 |
| #19151802 | 2 |
| #19151792 | 2 |
| #19151621 | 2 |
| #19151597 | 2 |
| #417×C89 | 2 |
| #3036 | 89 |