Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 90. #11758194 | Q16 | semidirect |
| 164. C61 | #9798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840141 | 2 |
| #21446809 | 2 |
| #21446807 | 2 |
| #21444577 | 2 |
| #21444499 | 2 |
| #21444100 | 2 |
| C61×#1548 | 2 |
| #9798 | 61 |