Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 168 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. #16840650 | C4 | semidirect |
| 8. C4×#11758187 | C4 | semidirect |
| 84. C61 | #12592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840650 | 2 |
| C2×C4×#11758187 | 2 |
| #21460857 | 2 |
| #21445506 | 2 |
| #12592 | 61 |