Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#15688918 | C2 | semidirect |
| 3. #20241549 | C2 | semidirect |
| 4. #20241546 | C2 | semidirect |
| 5. C2×C47×#355 | C2 | semidirect |
| 8. #15689673 | C4 | semidirect |
| 9. #15689518 | C4 | semidirect |
| 11. #15689513 | C4 | semidirect |
| 16. C4×#10625329 | C4 | semidirect |
| 37. #13094024 | C2×C4 | semidirect |
| 38. #13094021 | C2×C4 | semidirect |
| 45. #13093935 | C2×C4 | semidirect |
| 46. #13093935 | C2×C4 | semidirect |
| 171. C2×#355 | D47 | semidirect |
| 199. C47 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253852 | 2 |
| C2×#15688918 | 2 |
| #20241549 | 2 |
| #20241546 | 2 |
| C2×C47×#355 | 2 |
| #13578 | 47 |