Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
416 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 146 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. #20261601 | C2 | semidirect |
| 7. C2×#13095520 | C4 | semidirect |
| 10. C22×#11715897 | C4 | semidirect |
| 89. C97 | #1729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095520 | 2 |
| C23×#11715897 | 2 |
| #20261601 | 2 |
| C2×#15690766 | 2 |
| #1729 | 97 |