Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20241791 | C2 | semidirect |
| 5. #20241257 | C2 | semidirect |
| 6. #20241251 | C2 | semidirect |
| 7. C47×#1537 | C2 | semidirect |
| 162. #1537 | D47 | semidirect |
| 192. C47 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254395 | 2 |
| #20252466 | 2 |
| #20242084 | 2 |
| #20241791 | 2 |
| #20241257 | 2 |
| #20241251 | 2 |
| C47×#1537 | 2 |
| #9373 | 47 |