Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 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. #20245182 | C2 | semidirect |
| 5. #20244142 | C2 | semidirect |
| 6. #20241471 | C2 | semidirect |
| 7. C47×#1389 | C2 | semidirect |
| 18. #15688932 | C4 | semidirect |
| 144. #1389 | D47 | semidirect |
| 167. C47 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689244 | 2 |
| #20245182 | 2 |
| #20245123 | 2 |
| #20245117 | 2 |
| #20244142 | 2 |
| #20241471 | 2 |
| C47×#1389 | 2 |
| #12944 | 47 |