Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15668036 | C2 | semidirect |
| 2. #19152146 | C2 | semidirect |
| 3. C4×D4×D89 | C2 | semidirect |
| 4. #19151812 | C2 | semidirect |
| 5. #19151811 | C2 | semidirect |
| 6. #19151804 | C2 | semidirect |
| 7. #19151803 | C2 | semidirect |
| 8. #19151790 | C2 | semidirect |
| 9. #19151620 | C2 | semidirect |
| 10. #19151596 | C2 | semidirect |
| 11. #459×C89 | C2 | semidirect |
| 20. #15668012 | C22 | semidirect |
| 21. #15667999 | C22 | semidirect |
| 34. C4⋊#10623494 | C22 | semidirect |
| 35. #15667941 | C22 | semidirect |
| 36. #15667937 | C22 | semidirect |
| 37. #15667935 | C22 | semidirect |
| 38. #15667933 | C22 | semidirect |
| 40. #127×C89 | C22 | semidirect |
| 42. C4⋊C8×C89 | C22 | semidirect |
| 43. #102×C89 | C22 | semidirect |
| 52. D4×D89 | D4 | semidirect |
| 145. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 161. C89 | #3036 | semidirect |
| 170. #459 | D89 | semidirect |
| 183. #127 | C2×D89 | semidirect |
| 200. C4⋊C8 | C2×D89 | semidirect |
| 204. #102 | C2×D89 | semidirect |
| 311. C4 | #15668036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668036 | 2 |
| #19152146 | 2 |
| C4×D4×D89 | 2 |
| #19151812 | 2 |
| #19151811 | 2 |
| #19151804 | 2 |
| #19151803 | 2 |
| #19151790 | 2 |
| #19151620 | 2 |
| #19151596 | 2 |
| #459×C89 | 2 |
| #3036 | 89 |