Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1422 conjugacy classes of subgroups; only the 443 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 443 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 |
|---|---|---|
| 12. C42×Dic61 | C4 | semidirect |
| 50. C42×C61 | C4⋊C4 | semidirect |
| 88. Dic61 | #383 | semidirect |
| 109. C61 | #14688 | semidirect |
| 147. C42 | #11758196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839630 | 2 |
| C2×C42×Dic61 | 2 |
| #21444047 | 2 |
| #21444045 | 2 |
| C2×C61×#383 | 2 |
| #14688 | 61 |