Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×#16839588 | C2 | semidirect |
| 4. #21443929 | C2 | semidirect |
| 5. C2×C61×#368 | C2 | semidirect |
| 8. #16840178 | C4 | semidirect |
| 118. C2×#368 | D61 | semidirect |
| 142. C61 | #12842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840178 | 2 |
| C2×#16839588 | 2 |
| #21445880 | 2 |
| #21443929 | 2 |
| C2×C61×#368 | 2 |
| #12842 | 61 |