Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15690818 | C2 | semidirect |
| 3. #20261316 | C2 | semidirect |
| 4. #20261313 | C2 | semidirect |
| 5. #20260992 | C2 | semidirect |
| 6. #20260987 | C2 | semidirect |
| 7. #20260967 | C2 | semidirect |
| 8. #20260963 | C2 | semidirect |
| 9. C2×#15690741 | C2 | semidirect |
| 10. #20260737 | C2 | semidirect |
| 11. #417×C97 | C2 | semidirect |
| 63. C2×#11715895 | D4 | semidirect |
| 153. C97 | #3060 | semidirect |
| 164. #417 | 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×#15690818 | 2 |
| #20261316 | 2 |
| #20261313 | 2 |
| #20260992 | 2 |
| #20260987 | 2 |
| #20260967 | 2 |
| #20260963 | 2 |
| C2×#15690741 | 2 |
| #20260737 | 2 |
| #417×C97 | 2 |
| #3060 | 97 |