Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 4. C2×#15688927 | C2 | semidirect |
| 5. #20241498 | C2 | semidirect |
| 6. #20241477 | C2 | semidirect |
| 7. C47×#1979 | C2 | semidirect |
| 11. #15689564 | C4 | semidirect |
| 45. #13093964 | C2×C4 | semidirect |
| 60. C2×Q16×C47 | C2×C4 | semidirect |
| 180. #1979 | D47 | semidirect |
| 209. C47 | #13023 | semidirect |
| 222. C2×Q16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| #20252265 | 2 |
| C2×#15688929 | 2 |
| C2×#15688927 | 2 |
| #20241498 | 2 |
| #20241477 | 2 |
| C47×#1979 | 2 |
| #13023 | 47 |