Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 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. #20241982 | C2 | semidirect |
| 4. #20241810 | C2 | semidirect |
| 6. C8×#10625329 | C2 | semidirect |
| 7. C4×#108×C47 | C2 | semidirect |
| 172. C4×#108 | D47 | semidirect |
| 206. C47 | #9723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253947 | 2 |
| #20241982 | 2 |
| #20241979 | 2 |
| #20241810 | 2 |
| #20241806 | 2 |
| C8×#10625329 | 2 |
| C4×#108×C47 | 2 |
| #9723 | 47 |