Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20243190 | C2 | semidirect |
| 4. #20241516 | C2 | semidirect |
| 6. C2×#13094031 | C4 | semidirect |
| 10. #15689147 | C4 | semidirect |
| 12. #15689090 | C4 | semidirect |
| 15. C2×C4×C47⋊C8 | C4 | semidirect |
| 16. #15688922 | C4 | semidirect |
| 17. #15688920 | C4 | semidirect |
| 174. C47 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252100 | 2 |
| #20245073 | 2 |
| #20243190 | 2 |
| #20241516 | 2 |
| C47×#2126 | 2 |
| #12633 | 47 |