Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
596 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. #21461605 | C2 | semidirect |
| 2. #21461536 | C2 | semidirect |
| 3. C2×#16840618 | C2 | semidirect |
| 4. C2×#16840617 | C2 | semidirect |
| 31. #14519832 | D4 | semidirect |
| 234. C61 | #9689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461605 | 2 |
| #21461536 | 2 |
| C2×#16840618 | 2 |
| C2×#16840617 | 2 |
| #21454174 | 2 |
| #9689 | 61 |