Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20243518 | C2 | semidirect |
| 3. #20242134 | C2 | semidirect |
| 6. #20241248 | C2 | semidirect |
| 7. C47×#1286 | C2 | semidirect |
| 11. #15689200 | C4 | semidirect |
| 13. #15689188 | C4 | semidirect |
| 169. #1286 | D47 | semidirect |
| 195. C47 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252099 | 2 |
| #20243518 | 2 |
| #20242134 | 2 |
| #20241949 | 2 |
| #20241947 | 2 |
| #20241248 | 2 |
| C47×#1286 | 2 |
| #8678 | 47 |