Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
508 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20246108 | C2 | semidirect |
| 5. #20241248 | C2 | semidirect |
| 6. #20241216 | C2 | semidirect |
| 7. C47×#1546 | C2 | semidirect |
| 10. #15689526 | C4 | semidirect |
| 11. #15689471 | C4 | semidirect |
| 185. #1546 | D47 | semidirect |
| 214. C47 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254509 | 2 |
| #20246108 | 2 |
| #20244219 | 2 |
| #20241949 | 2 |
| #20241248 | 2 |
| #20241216 | 2 |
| C47×#1546 | 2 |
| #9300 | 47 |