Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #20259894 | C2 | semidirect |
| 2. #20259892 | C2 | semidirect |
| 3. #20259889 | C2 | semidirect |
| 4. #20259885 | C2 | semidirect |
| 5. #20259884 | C2 | semidirect |
| 6. #20259881 | C2 | semidirect |
| 7. #20259877 | C2 | semidirect |
| 9. C4×Dic386 | C2 | semidirect |
| 10. C4×D772 | C2 | semidirect |
| 11. C4×C22⋊D193 | C2 | semidirect |
| 12. C4×C22⋊D193 | C2 | semidirect |
| 13. #20259856 | C2 | semidirect |
| 14. C42×D193 | C2 | semidirect |
| 15. #117×C193 | C2 | semidirect |
| 103. C193 | #529 | semidirect |
| 118. #117 | D193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259894 | 2 |
| #20259892 | 2 |
| #20259889 | 2 |
| #20259885 | 2 |
| #20259884 | 2 |
| #20259881 | 2 |
| #20259877 | 2 |
| #20259872 | 2 |
| C4×Dic386 | 2 |
| C4×D772 | 2 |
| C4×C22⋊D193 | 2 |
| #20259856 | 2 |
| C42×D193 | 2 |
| #117×C193 | 2 |
| #529 | 193 |