Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#15688960 | C2 | semidirect |
| 2. C2×D1504 | C2 | semidirect |
| 3. C2×#15688958 | C2 | semidirect |
| 4. #20245650 | C2 | semidirect |
| 5. #20245636 | C2 | semidirect |
| 6. #20241521 | C2 | semidirect |
| 7. C2×C47×SD64 | C2 | semidirect |
| 37. C47⋊C32 | D4 | semidirect |
| 45. C32×C47 | D4 | semidirect |
| 99. C2×SD64 | D47 | semidirect |
| 125. C47 | #13729 | semidirect |
| 148. C32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688960 | 2 |
| C2×D1504 | 2 |
| C2×#15688958 | 2 |
| #20245650 | 2 |
| #20245636 | 2 |
| #20241521 | 2 |
| C2×C47×SD64 | 2 |
| #13729 | 47 |