Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 7. #16840657 | C4 | semidirect |
| 11. C2×#14519713 | C4 | semidirect |
| 14. C2×#108×C61 | C4 | semidirect |
| 146. C2×#108 | #6923 | semidirect |
| 153. C61 | #7260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840657 | 2 |
| #21461505 | 2 |
| #21445854 | 2 |
| #7260 | 61 |