Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#15690832 | C2 | semidirect |
| 2. C2×#15690829 | C2 | semidirect |
| 3. #20261403 | C2 | semidirect |
| 4. #20261110 | C2 | semidirect |
| 5. #20260972 | C2 | semidirect |
| 6. #20260934 | C2 | semidirect |
| 7. #20260881 | C2 | semidirect |
| 8. #20260878 | C2 | semidirect |
| 9. #20260829 | C2 | semidirect |
| 10. C8×C22⋊D97 | C2 | semidirect |
| 11. #466×C97 | C2 | semidirect |
| 56. Dic388 | D4 | semidirect |
| 134. Dic97 | #135 | semidirect |
| 143. C97 | #3287 | semidirect |
| 149. #466 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690829 | 2 |
| #20261403 | 2 |
| #20261110 | 2 |
| #20260972 | 2 |
| #20260934 | 2 |
| #20260881 | 2 |
| #20260878 | 2 |
| #20260829 | 2 |
| C8×C22⋊D97 | 2 |
| #466×C97 | 2 |
| #3287 | 97 |