Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 2. #20244366 | C2 | semidirect |
| 4. C4×C8×Dic47 | C2 | semidirect |
| 5. #20242143 | C2 | semidirect |
| 7. C47×#1493 | C2 | semidirect |
| 9. #15689519 | C4 | semidirect |
| 10. #15689497 | C4 | semidirect |
| 11. #15689473 | C4 | semidirect |
| 12. #15689471 | C4 | semidirect |
| 104. C4×Dic47 | SD16 | semidirect |
| 141. C47⋊C8 | #104 | semidirect |
| 166. #1493 | D47 | semidirect |
| 192. C47 | #9843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253948 | 2 |
| #20244366 | 2 |
| #20244215 | 2 |
| C4×C8×Dic47 | 2 |
| #20242143 | 2 |
| #20241840 | 2 |
| C47×#1493 | 2 |
| #9843 | 47 |