Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 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. #20252299 | C2 | semidirect |
| 2. #20245600 | C2 | semidirect |
| 3. #20245556 | C2 | semidirect |
| 4. #20245461 | C2 | semidirect |
| 5. #20245333 | C2 | semidirect |
| 6. #20245284 | C2 | semidirect |
| 7. #20245200 | C2 | semidirect |
| 8. C47×#3184 | C2 | semidirect |
| 18. #15688945 | C22 | semidirect |
| 19. #15688944 | C22 | semidirect |
| 20. #15688936 | C22 | semidirect |
| 23. #15688901 | C22 | semidirect |
| 25. C47×#498 | C22 | semidirect |
| 26. C47×#493 | C22 | semidirect |
| 31. C47×#442 | C22 | semidirect |
| 107. Dic188 | #41 | semidirect |
| 109. D376 | #41 | semidirect |
| 165. #3184 | D47 | semidirect |
| 182. #498 | C2×D47 | semidirect |
| 183. #493 | C2×D47 | semidirect |
| 192. #442 | C2×D47 | semidirect |
| 202. C47 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252299 | 2 |
| #20245600 | 2 |
| #20245556 | 2 |
| #20245461 | 2 |
| #20245333 | 2 |
| #20245284 | 2 |
| #20245200 | 2 |
| C47×#3184 | 2 |
| #33688 | 47 |