Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
842 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 216 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. C4×C4⋊#6923 | C4 | semidirect |
| 14. C2×#14519688 | C4 | semidirect |
| 15. C2×C8×Dic61 | C4 | semidirect |
| 16. C2×#97×C61 | C4 | semidirect |
| 63. C2×C8×C61 | C4⋊C4 | semidirect |
| 73. C2×#92418 | C4⋊C4 | semidirect |
| 120. Dic61 | H(3,ℤ/4) | semidirect |
| 137. C2×#97 | #6923 | semidirect |
| 144. C61 | #10837 | semidirect |
| 191. C2×C8 | C4⋊#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462268 | 2 |
| C2×#16840630 | 2 |
| C2×#16839714 | 2 |
| #10837 | 61 |