Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #20245146 | C2 | semidirect |
| 5. #20243511 | C2 | semidirect |
| 6. #20241499 | C2 | semidirect |
| 7. C47×#1382 | C2 | semidirect |
| 11. #15689244 | C4 | semidirect |
| 142. #1382 | D47 | semidirect |
| 164. C47 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252304 | 2 |
| #20245146 | 2 |
| #20245123 | 2 |
| C2×#15688931 | 2 |
| #20243511 | 2 |
| #20241499 | 2 |
| C47×#1382 | 2 |
| #12830 | 47 |