Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19152268 | C2 | semidirect |
| 3. #19152233 | C2 | semidirect |
| 4. #19151848 | C2 | semidirect |
| 5. #19151795 | C2 | semidirect |
| 6. #19151790 | C2 | semidirect |
| 7. #19151740 | C2 | semidirect |
| 8. #19151730 | C2 | semidirect |
| 9. C4×#13083563 | C2 | semidirect |
| 10. #19151677 | C2 | semidirect |
| 11. #493×C89 | C2 | semidirect |
| 12. C2×#13083573 | C22 | semidirect |
| 17. C2×#13083562 | C22 | semidirect |
| 19. C2×#13083557 | C22 | semidirect |
| 24. #15667983 | C22 | semidirect |
| 26. C4×Dic178 | C22 | semidirect |
| 30. #15667944 | C22 | semidirect |
| 31. C4⋊#10623494 | C22 | semidirect |
| 32. #15667937 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667933 | C22 | semidirect |
| 36. #15667924 | C22 | semidirect |
| 37. C2×D8×C89 | C22 | semidirect |
| 38. C2×D8×C89 | C22 | semidirect |
| 40. #127×C89 | C22 | semidirect |
| 41. C4×C8×C89 | C22 | semidirect |
| 58. #13083563 | D4 | semidirect |
| 117. Dic178 | C2×D4 | semidirect |
| 119. C8×C89 | C2×D4 | semidirect |
| 136. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 151. C89 | #3274 | semidirect |
| 155. #493 | D89 | semidirect |
| 170. C2×D8 | C2×D89 | semidirect |
| 171. C2×D8 | C2×D89 | semidirect |
| 175. #127 | C2×D89 | semidirect |
| 192. C4×C8 | C2×D89 | semidirect |
| 271. C8 | D4×D89 | semidirect |
| 291. 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 |
| #19152268 | 2 |
| #19152233 | 2 |
| #19151848 | 2 |
| #19151795 | 2 |
| #19151790 | 2 |
| #19151740 | 2 |
| #19151730 | 2 |
| C4×#13083563 | 2 |
| #19151677 | 2 |
| #493×C89 | 2 |
| #3274 | 89 |