Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 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. #20244368 | C2 | semidirect |
| 3. #20242116 | C2 | semidirect |
| 4. #20242025 | C2 | semidirect |
| 5. #20241901 | C2 | semidirect |
| 12. #15689843 | C4 | semidirect |
| 14. D4×Dic94 | C4 | semidirect |
| 239. C47 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257802 | 2 |
| #20244368 | 2 |
| #20242116 | 2 |
| #20242025 | 2 |
| #20241901 | 2 |
| #20241896 | 2 |
| C47×#1557 | 2 |
| #8496 | 47 |