Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 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. #20254102 | C2 | semidirect |
| 2. #20253781 | C2 | semidirect |
| 3. #20253769 | C2 | semidirect |
| 4. #20243038 | C2 | semidirect |
| 5. #20243032 | C2 | semidirect |
| 6. #20243026 | C2 | semidirect |
| 7. #20242999 | C2 | semidirect |
| 8. #20241691 | C2 | semidirect |
| 197. C47 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254102 | 2 |
| #20253781 | 2 |
| #20253769 | 2 |
| #20243038 | 2 |
| #20243032 | 2 |
| #20243026 | 2 |
| #20242999 | 2 |
| #20241691 | 2 |
| C47×#3184 | 2 |
| #19754 | 47 |