Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #21446767 | C2 | semidirect |
| 4. #21443660 | C2 | semidirect |
| 9. #16840134 | C4 | semidirect |
| 28. #14519777 | C2×C4 | semidirect |
| 33. C4×#92418 | C2×C4 | semidirect |
| 74. C4⋊C4×C61 | SD16 | semidirect |
| 172. C61 | #9064 | semidirect |
| 236. C4⋊C4 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840134 | 2 |
| #21446767 | 2 |
| C2×#16839506 | 2 |
| #21443660 | 2 |
| C61×#2366 | 2 |
| #9064 | 61 |