Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
374 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 23. #14519847 | C8 | semidirect |
| 79. #92420 | #108 | semidirect |
| 121. C61 | C8×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519847 | 2 |
| #21461021 | 2 |
| C8×D61⋊C8 | 2 |
| #21460650 | 2 |
| #21444564 | 2 |
| C8×#108 | 61 |