Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1618 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 267 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. C2×#16840152 | C2 | semidirect |
| 2. C2×#16840149 | C2 | semidirect |
| 3. C2×#16840144 | C2 | semidirect |
| 4. C2×#16840138 | C2 | semidirect |
| 5. #21451925 | C2 | semidirect |
| 6. #21445506 | C2 | semidirect |
| 7. C61×#2657 | C2 | semidirect |
| 46. #14519688 | D4 | semidirect |
| 47. C4×#92418 | D4 | semidirect |
| 138. #2657 | D61 | semidirect |
| 162. C61 | #33308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840152 | 2 |
| C2×#16840149 | 2 |
| C2×#16840144 | 2 |
| C2×#16840138 | 2 |
| #21451925 | 2 |
| #21445506 | 2 |
| C61×#2657 | 2 |
| #33308 | 61 |