Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15688948 | C2 | semidirect |
| 5. #20241497 | C2 | semidirect |
| 6. #20241483 | C2 | semidirect |
| 7. C47×#2159 | C2 | semidirect |
| 19. #15688908 | C4 | semidirect |
| 43. C2×C47⋊C16 | C2×C4 | semidirect |
| 56. M32×C47 | C2×C4 | semidirect |
| 153. #2159 | D47 | semidirect |
| 183. C47 | #12925 | semidirect |
| 203. M32 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251985 | 2 |
| C2×#15688948 | 2 |
| C2×#15688908 | 2 |
| #20243453 | 2 |
| #20241497 | 2 |
| #20241483 | 2 |
| C47×#2159 | 2 |
| #12925 | 47 |