Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
454 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 454 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. #20246681 | C2 | semidirect |
| 3. #20241289 | C2 | semidirect |
| 4. #20241217 | C2 | semidirect |
| 36. C4⋊Q8×C47 | Q8 | semidirect |
| 37. #127×C47 | Q8 | semidirect |
| 159. C47 | #10370 | semidirect |
| 163. C4⋊Q8 | Dic94 | semidirect |
| 164. #127 | Dic94 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20246681 | 2 |
| #20241883 | 2 |
| #20241289 | 2 |
| #20241217 | 2 |
| C47×#1963 | 2 |
| #10370 | 47 |