Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15690830 | C2 | semidirect |
| 2. C2×#15690817 | C2 | semidirect |
| 3. #20261313 | C2 | semidirect |
| 4. #20260991 | C2 | semidirect |
| 5. #20260986 | C2 | semidirect |
| 6. #20260966 | C2 | semidirect |
| 7. #20260962 | C2 | semidirect |
| 8. C2×#15690741 | C2 | semidirect |
| 9. #20260736 | C2 | semidirect |
| 10. #20260734 | C2 | semidirect |
| 11. #537×C97 | C2 | semidirect |
| 58. C2×#11715895 | D4 | semidirect |
| 153. C97 | #3060 | semidirect |
| 157. #537 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690830 | 2 |
| C2×#15690817 | 2 |
| #20261313 | 2 |
| #20260991 | 2 |
| #20260986 | 2 |
| #20260966 | 2 |
| #20260962 | 2 |
| C2×#15690741 | 2 |
| #20260736 | 2 |
| #20260734 | 2 |
| #537×C97 | 2 |
| #3060 | 97 |