Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #20241444 | C2 | semidirect |
| 5. #20241442 | C2 | semidirect |
| 6. #20241437 | C2 | semidirect |
| 7. C47×#1362 | C2 | semidirect |
| 130. #1362 | D47 | semidirect |
| 152. C47 | #11954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253972 | 2 |
| #20245190 | 2 |
| #335×D47 | 2 |
| #20241444 | 2 |
| #20241442 | 2 |
| #20241437 | 2 |
| C47×#1362 | 2 |
| #11954 | 47 |