Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 7. #15690865 | C4 | semidirect |
| 8. C4×#11715897 | C4 | semidirect |
| 60. C97 | #1746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690865 | 2 |
| C2×C4×#11715897 | 2 |
| #20261601 | 2 |
| #20260580 | 2 |
| #1746 | 97 |