Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 9. #16840628 | C4 | semidirect |
| 12. C2×#14519688 | C4 | semidirect |
| 14. C2×#97×C61 | C4 | semidirect |
| 164. C2×#97 | #6923 | semidirect |
| 170. C61 | #7036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461546 | 2 |
| #21460995 | 2 |
| #21445582 | 2 |
| #7036 | 61 |