Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 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×#15689540 | C2 | semidirect |
| 3. #20245115 | C2 | semidirect |
| 4. C2×#15688929 | C2 | semidirect |
| 5. C47×#2916 | C2 | semidirect |
| 13. C2×#13093964 | C22 | semidirect |
| 14. C22×C47⋊C16 | C22 | semidirect |
| 15. #15688929 | C22 | semidirect |
| 16. #15688929 | C22 | semidirect |
| 20. C2×#108×C47 | C22 | semidirect |
| 115. #2916 | D47 | semidirect |
| 134. C2×#108 | C2×D47 | semidirect |
| 137. C47 | #33385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258162 | 2 |
| C2×#15689540 | 2 |
| #20245115 | 2 |
| C2×#15688929 | 2 |
| C47×#2916 | 2 |
| #33385 | 47 |