Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #20241887 | C2 | semidirect |
| 5. #20241290 | C2 | semidirect |
| 6. #20241246 | C2 | semidirect |
| 7. C47×#1518 | C2 | semidirect |
| 10. #15689410 | C4 | semidirect |
| 11. #15689400 | C4 | semidirect |
| 187. #1518 | D47 | semidirect |
| 219. C47 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253181 | 2 |
| #20246363 | 2 |
| #20241887 | 2 |
| #20241780 | 2 |
| #20241290 | 2 |
| #20241246 | 2 |
| C47×#1518 | 2 |
| #9177 | 47 |