Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
662 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20252297 | C2 | semidirect |
| 2. #20252025 | C2 | semidirect |
| 3. #20244903 | C2 | semidirect |
| 4. #20244675 | C2 | semidirect |
| 6. #20244055 | C2 | semidirect |
| 7. #20243835 | C2 | semidirect |
| 8. #20243805 | C2 | semidirect |
| 9. #20243629 | C2 | semidirect |
| 10. #20243535 | C2 | semidirect |
| 11. C47×#2102 | C2 | semidirect |
| 73. #13093934 | D4 | semidirect |
| 75. C8×Dic47 | D4 | semidirect |
| 192. #2102 | D47 | semidirect |
| 233. C47 | #29385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252297 | 2 |
| #20252025 | 2 |
| #20244903 | 2 |
| #20244675 | 2 |
| #20244456 | 2 |
| #20244055 | 2 |
| #20243835 | 2 |
| #20243805 | 2 |
| #20243629 | 2 |
| #20243535 | 2 |
| C47×#2102 | 2 |
| #29385 | 47 |