Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
612 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244331 | C2 | semidirect |
| 3. #20241899 | C2 | semidirect |
| 5. #20241281 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 10. #15689403 | C4 | semidirect |
| 11. #15689328 | C4 | semidirect |
| 31. #13094024 | C2×C4 | semidirect |
| 32. #13094024 | C2×C4 | semidirect |
| 41. C4⋊(C47⋊C8) | C2×C4 | semidirect |
| 214. C47 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253487 | 2 |
| #20244331 | 2 |
| #20241899 | 2 |
| #20241831 | 2 |
| #20241281 | 2 |
| #20241244 | 2 |
| C47×#2275 | 2 |
| #9323 | 47 |