Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C2×C4⋊C4×D89 | C2 | semidirect |
| 3. #19151913 | C2 | semidirect |
| 4. #19151912 | C2 | semidirect |
| 5. #19151911 | C2 | semidirect |
| 6. #19151910 | C2 | semidirect |
| 7. #19151909 | C2 | semidirect |
| 8. #107×D89 | C2 | semidirect |
| 9. #102×D89 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #480×C89 | C2 | semidirect |
| 22. C2×C4⋊Dic89 | C22 | semidirect |
| 28. C4⋊C4×D89 | C22 | semidirect |
| 30. #15667946 | C22 | semidirect |
| 31. #15667945 | C22 | semidirect |
| 32. #15667945 | C22 | semidirect |
| 33. #15667934 | C22 | semidirect |
| 34. #15667933 | C22 | semidirect |
| 35. #15667932 | C22 | semidirect |
| 36. C22⋊#10623494 | C22 | semidirect |
| 37. #15667924 | C22 | semidirect |
| 39. C2×C4⋊C4×C89 | C22 | semidirect |
| 40. #107×C89 | C22 | semidirect |
| 41. #102×C89 | C22 | semidirect |
| 42. C22⋊C8×C89 | C22 | semidirect |
| 155. D89 | #480 | direct (N × H) |
| 157. C89 | C2×#480 | semidirect |
| 165. #480 | D89 | direct (N × H) |
| 187. C2×C4⋊C4 | C2×D89 | semidirect |
| 192. #107 | C2×D89 | semidirect |
| 196. #102 | C2×D89 | semidirect |
| 199. C22⋊C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D89 | 2 |
| C2×C4⋊C4×D89 | 2 |
| #19151913 | 2 |
| #19151912 | 2 |
| #19151911 | 2 |
| #19151910 | 2 |
| #19151909 | 2 |
| #107×D89 | 2 |
| #102×D89 | 2 |
| C22⋊C8×D89 | 2 |
| #480×C89 | 2 |
| C2×#480 | 89 |