Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20261087 | C2 | semidirect |
| 4. #20261072 | C2 | semidirect |
| 5. #20260977 | C2 | semidirect |
| 6. #20260946 | C2 | semidirect |
| 7. #20260892 | C2 | semidirect |
| 8. C4×#13095501 | C2 | semidirect |
| 10. #103×D97 | C2 | semidirect |
| 11. #477×C97 | C2 | semidirect |
| 90. D388 | Q16 | semidirect |
| 123. C97 | #3299 | semidirect |
| 128. #477 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261446 | 2 |
| Q8×D388 | 2 |
| #20261087 | 2 |
| #20261072 | 2 |
| #20260977 | 2 |
| #20260946 | 2 |
| #20260892 | 2 |
| C4×#13095501 | 2 |
| #20260800 | 2 |
| #103×D97 | 2 |
| #477×C97 | 2 |
| #3299 | 97 |