Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20256490 | C2 | semidirect |
| 3. C2×#15688937 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. #20243435 | C2 | semidirect |
| 6. #20241504 | C2 | semidirect |
| 7. C47×#1389 | C2 | semidirect |
| 47. #13093964 | D4 | semidirect |
| 60. M32×C47 | D4 | semidirect |
| 169. #1389 | D47 | semidirect |
| 194. C47 | #13079 | semidirect |
| 222. M32 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256490 | 2 |
| #20253037 | 2 |
| C2×#15688937 | 2 |
| C2×#15688935 | 2 |
| #20243435 | 2 |
| #20241504 | 2 |
| C47×#1389 | 2 |
| #13079 | 47 |