Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668042 | C2 | semidirect |
| 2. C2×#15668037 | C2 | semidirect |
| 3. C22×#13083563 | C2 | semidirect |
| 4. #19152169 | C2 | semidirect |
| 5. #19152162 | C2 | semidirect |
| 6. #19151991 | C2 | semidirect |
| 7. #19151986 | C2 | semidirect |
| 8. #19151979 | C2 | semidirect |
| 9. #19151969 | C2 | semidirect |
| 10. #19151553 | C2 | semidirect |
| 11. C2×#135×C89 | C2 | semidirect |
| 16. C2×#13083564 | C22 | semidirect |
| 20. C2×#13083562 | C22 | semidirect |
| 24. #15668010 | C22 | semidirect |
| 27. #15667999 | C22 | semidirect |
| 33. #15667922 | C22 | semidirect |
| 34. C8×Dic89 | C22 | semidirect |
| 38. C2×Q16×C89 | C22 | semidirect |
| 39. C2×SD16×C89 | C22 | semidirect |
| 40. C2×SD16×C89 | C22 | semidirect |
| 41. C2×D8×C89 | C22 | semidirect |
| 60. #13083558 | D4 | semidirect |
| 85. C2×C8×C89 | D4 | semidirect |
| 149. C89 | #3154 | semidirect |
| 152. C2×#135 | D89 | semidirect |
| 169. C2×Q16 | C2×D89 | semidirect |
| 175. C2×SD16 | C2×D89 | semidirect |
| 176. C2×SD16 | C2×D89 | semidirect |
| 178. C2×D8 | C2×D89 | semidirect |
| 228. C2×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668042 | 2 |
| C2×#15668037 | 2 |
| C22×#13083563 | 2 |
| #19152169 | 2 |
| #19152162 | 2 |
| #19151991 | 2 |
| #19151986 | 2 |
| #19151979 | 2 |
| #19151969 | 2 |
| #19151553 | 2 |
| C2×#135×C89 | 2 |
| #3154 | 89 |