Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20246568 | C2 | semidirect |
| 3. #20242104 | C2 | semidirect |
| 6. #20241253 | C2 | semidirect |
| 7. C47×#1288 | C2 | semidirect |
| 11. #15689474 | C4 | semidirect |
| 12. #15689470 | C4 | semidirect |
| 152. #1288 | D47 | semidirect |
| 175. C47 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253782 | 2 |
| #20246568 | 2 |
| #20242104 | 2 |
| #20241936 | 2 |
| #20241934 | 2 |
| #20241253 | 2 |
| C47×#1288 | 2 |
| #9430 | 47 |