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. #20255792 | C2 | semidirect |
| 2. #20245667 | C2 | semidirect |
| 3. #20245577 | C2 | semidirect |
| 4. #20245567 | C2 | semidirect |
| 5. #20245545 | C2 | semidirect |
| 6. #20245488 | C2 | semidirect |
| 7. #20245221 | C2 | semidirect |
| 8. #20245173 | C2 | semidirect |
| 9. C4×D16×C47 | C2 | semidirect |
| 140. C4×D16 | 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 |
|---|---|
| #20255792 | 2 |
| #20245667 | 2 |
| #20245577 | 2 |
| #20245567 | 2 |
| #20245545 | 2 |
| #20245488 | 2 |
| #20245221 | 2 |
| #20245173 | 2 |
| C4×D16×C47 | 2 |
| #33922 | 47 |