Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
954 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 268 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. #16840698 | C4 | semidirect |
| 8. C42×#6923 | C4 | semidirect |
| 9. #16840630 | C4 | direct (N × H) |
| 13. C2×#14519687 | C4 | semidirect |
| 14. C2×C4×#92418 | C4 | semidirect |
| 15. C2×C4×C8×C61 | C4 | semidirect |
| 56. C4×#6923 | C42 | semidirect |
| 59. C2×C8×C61 | C42 | semidirect |
| 69. C2×#92418 | C42 | semidirect |
| 104. C4×C61 | H(3,ℤ/4) | semidirect |
| 123. C2×C4×C8 | #6923 | semidirect |
| 129. C61 | C4×H(3,ℤ/4) | semidirect |
| 172. C2×C8 | C4×#6923 | semidirect |
| 219. C4 | #16840630 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519856 | 2 |
| C2×#16840630 | 2 |
| C2×C4×#11758189 | 2 |
| C4×H(3,ℤ/4) | 61 |