Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 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. #20255789 | C2 | semidirect |
| 2. #20245582 | C2 | semidirect |
| 3. #20245570 | C2 | semidirect |
| 4. #20245542 | C2 | semidirect |
| 5. #20245492 | C2 | semidirect |
| 6. C4×D752 | C2 | semidirect |
| 7. #20245221 | C2 | semidirect |
| 8. #20245175 | C2 | semidirect |
| 9. C47×#2253 | C2 | semidirect |
| 135. #2253 | D47 | semidirect |
| 173. C47 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255789 | 2 |
| #20245582 | 2 |
| #20245570 | 2 |
| #20245542 | 2 |
| #20245492 | 2 |
| C4×D752 | 2 |
| #20245221 | 2 |
| #20245175 | 2 |
| C47×#2253 | 2 |
| #33922 | 47 |