Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
640 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 108 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. #21461604 | C2 | semidirect |
| 2. C4×#14519832 | C2 | semidirect |
| 3. C2×#16840618 | C2 | semidirect |
| 4. C2×#16840617 | C2 | semidirect |
| 32. #14519832 | D4 | semidirect |
| 202. Dic61 | #329 | semidirect |
| 236. C61 | #9685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461604 | 2 |
| C4×#14519832 | 2 |
| C2×#16840618 | 2 |
| C2×#16840617 | 2 |
| #21454174 | 2 |
| #9685 | 61 |