Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
590 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 159 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×#16839562 | C2 | semidirect |
| 3. C2×#16839538 | C2 | semidirect |
| 4. C61×#1846 | C2 | semidirect |
| 10. #16840139 | C4 | semidirect |
| 30. C2×#11758185 | D4 | semidirect |
| 108. #1846 | D61 | semidirect |
| 126. C61 | #13206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840139 | 2 |
| C2×#16839562 | 2 |
| C2×#16839538 | 2 |
| C61×#1846 | 2 |
| #13206 | 61 |