Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
626 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 8. #16840631 | C4 | semidirect |
| 147. C61 | #10815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461524 | 2 |
| #21461511 | 2 |
| C2×#16840631 | 2 |
| C2×#16839719 | 2 |
| #10815 | 61 |