Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
320 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 320 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 |
|---|---|---|
| 19. #14519844 | C8 | semidirect |
| 137. C61 | #7022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461604 | 2 |
| C4×#14519844 | 2 |
| #21445934 | 2 |
| #7022 | 61 |