Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 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. #20244221 | C2 | semidirect |
| 3. #20242119 | C2 | semidirect |
| 4. #20242111 | C2 | semidirect |
| 5. #20241901 | C2 | semidirect |
| 6. #20241897 | C2 | semidirect |
| 7. C47×#1536 | C2 | semidirect |
| 9. #15689834 | C4 | semidirect |
| 12. #15689793 | C4 | semidirect |
| 220. #1536 | D47 | semidirect |
| 254. C47 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257786 | 2 |
| #20244221 | 2 |
| #20242119 | 2 |
| #20242111 | 2 |
| #20241901 | 2 |
| #20241897 | 2 |
| C47×#1536 | 2 |
| #8493 | 47 |