Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
340 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #20241564 | C2 | direct (N × H) |
| 5. C2×#13094016 | C4 | semidirect |
| 8. #15689477 | C4 | semidirect |
| 13. C2×C4×C47⋊C8 | C4 | semidirect |
| 23. #13094016 | C2×C4 | semidirect |
| 34. C4×C47⋊C8 | C2×C4 | semidirect |
| 138. C2×C47 | #1414 | semidirect |
| 155. C47 | C2×#1414 | semidirect |
| 269. C2 | #20241564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689477 | 2 |
| C2×#15688918 | 2 |
| #20241564 | 2 |
| C2×C47×#355 | 2 |
| C2×#1414 | 47 |