Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #20245182 | C2 | semidirect |
| 5. #20241501 | C2 | semidirect |
| 6. #20241470 | C2 | semidirect |
| 7. C4×#108×C47 | C2 | semidirect |
| 15. #15688938 | C4 | semidirect |
| 16. #15688935 | C4 | semidirect |
| 141. C4×#108 | D47 | semidirect |
| 164. C47 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245182 | 2 |
| #20245135 | 2 |
| #20245115 | 2 |
| #20244276 | 2 |
| #20241501 | 2 |
| #20241470 | 2 |
| C4×#108×C47 | 2 |
| #13137 | 47 |