Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
658 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 8. #16840630 | C4 | semidirect |
| 13. C2×#14519687 | C4 | semidirect |
| 14. C2×C4×#92418 | C4 | semidirect |
| 15. C2×C8×Dic61 | C4 | semidirect |
| 16. C2×#97×C61 | C4 | semidirect |
| 143. C2×#97 | #6923 | semidirect |
| 149. C61 | #10814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461518 | 2 |
| #21461505 | 2 |
| C2×#16840630 | 2 |
| C2×#16839719 | 2 |
| #10814 | 61 |