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×#15668043 | C2 | semidirect |
| 2. C2×#15668037 | C2 | semidirect |
| 3. C2×#15668032 | C2 | semidirect |
| 4. C22×#13083561 | C2 | semidirect |
| 5. #19152167 | C2 | semidirect |
| 6. #19151990 | C2 | semidirect |
| 7. #19151988 | C2 | semidirect |
| 8. #19151980 | C2 | semidirect |
| 9. #19151972 | C2 | semidirect |
| 10. #19151554 | C2 | semidirect |
| 11. #536×C89 | C2 | semidirect |
| 17. C2×#13083564 | C22 | semidirect |
| 18. C2×#13083564 | C22 | semidirect |
| 19. C2×#13083562 | C22 | semidirect |
| 24. C2×#13083561 | C22 | semidirect |
| 25. C2×#13083561 | C22 | semidirect |
| 27. C2×#13083559 | C22 | semidirect |
| 34. #15667923 | C22 | semidirect |
| 35. C4×#10623494 | C22 | semidirect |
| 38. C4⋊Q8×C89 | C22 | semidirect |
| 39. #124×C89 | C22 | semidirect |
| 65. #13083558 | D4 | semidirect |
| 66. C2×#10623494 | D4 | semidirect |
| 149. C89 | #3154 | semidirect |
| 154. #536 | D89 | semidirect |
| 181. C4⋊Q8 | C2×D89 | semidirect |
| 184. #124 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668043 | 2 |
| C2×#15668037 | 2 |
| C2×#15668032 | 2 |
| C22×#13083561 | 2 |
| #19152167 | 2 |
| #19151990 | 2 |
| #19151988 | 2 |
| #19151980 | 2 |
| #19151972 | 2 |
| #19151554 | 2 |
| #536×C89 | 2 |
| #3154 | 89 |