Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 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×#15688938 | C2 | semidirect |
| 5. #20245107 | C2 | semidirect |
| 6. #20244993 | C2 | semidirect |
| 7. C47×#1833 | C2 | semidirect |
| 15. #15689507 | C4 | semidirect |
| 16. #15689503 | C4 | semidirect |
| 170. #1833 | D47 | semidirect |
| 195. C47 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253882 | 2 |
| C2×#15688938 | 2 |
| #20245123 | 2 |
| #20245115 | 2 |
| #20245107 | 2 |
| #20244993 | 2 |
| C47×#1833 | 2 |
| #13216 | 47 |