Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20254771 | C2 | semidirect |
| 3. #20242528 | C2 | semidirect |
| 4. #20242509 | C2 | semidirect |
| 5. #20242466 | C2 | semidirect |
| 6. #20242447 | C2 | semidirect |
| 7. #20242123 | C2 | semidirect |
| 8. #20241843 | C2 | semidirect |
| 9. C47×#3550 | C2 | semidirect |
| 186. #3550 | D47 | semidirect |
| 227. C47 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254771 | 2 |
| #20253814 | 2 |
| #20242528 | 2 |
| #20242509 | 2 |
| #20242466 | 2 |
| #20242447 | 2 |
| #20242123 | 2 |
| #20241843 | 2 |
| C47×#3550 | 2 |
| #18688 | 47 |