Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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. #108×Dic47 | C2 | semidirect |
| 5. #20241499 | C2 | semidirect |
| 6. #20241469 | C2 | semidirect |
| 7. C47×#2161 | C2 | semidirect |
| 15. #15688940 | C4 | semidirect |
| 16. #15688937 | C4 | semidirect |
| 137. #2161 | D47 | semidirect |
| 164. C47 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245138 | 2 |
| #20245115 | 2 |
| #20244274 | 2 |
| #108×Dic47 | 2 |
| #20241499 | 2 |
| #20241469 | 2 |
| C47×#2161 | 2 |
| #13137 | 47 |