Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
430 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 11. #16840624 | C4 | semidirect |
| 12. #16840603 | C4 | semidirect |
| 32. #14519710 | C8 | semidirect |
| 87. #92418 | C4×C8 | semidirect |
| 125. C61 | #8284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊C4×#92420 | 2 |
| C2×#16840624 | 2 |
| C2×#16840603 | 2 |
| #21460655 | 2 |
| #21445711 | 2 |
| #8284 | 61 |