Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
954 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 163 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. #20257802 | C2 | semidirect |
| 2. #20254775 | C2 | semidirect |
| 3. #20242526 | C2 | semidirect |
| 4. #20242507 | C2 | semidirect |
| 5. #20242464 | C2 | semidirect |
| 6. #20242445 | C2 | semidirect |
| 7. #20242123 | C2 | semidirect |
| 8. #20241844 | C2 | semidirect |
| 227. C47 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257802 | 2 |
| #20254775 | 2 |
| #20242526 | 2 |
| #20242507 | 2 |
| #20242464 | 2 |
| #20242445 | 2 |
| #20242123 | 2 |
| #20241844 | 2 |
| C47×#3147 | 2 |
| #18688 | 47 |