Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 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. C2×#15688935 | C2 | semidirect |
| 3. #20245123 | C2 | semidirect |
| 4. #20245115 | C2 | semidirect |
| 5. #20245103 | C2 | semidirect |
| 6. #20244993 | C2 | semidirect |
| 7. C47×#1833 | C2 | semidirect |
| 15. #15689507 | C4 | semidirect |
| 16. #15689500 | C4 | semidirect |
| 53. #13093964 | D4 | semidirect |
| 55. C2×C47⋊C16 | D4 | semidirect |
| 175. #1833 | D47 | semidirect |
| 201. C47 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253874 | 2 |
| C2×#15688935 | 2 |
| #20245123 | 2 |
| #20245115 | 2 |
| #20245103 | 2 |
| #20244993 | 2 |
| C47×#1833 | 2 |
| #13215 | 47 |