Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. #21461762 | C2 | semidirect |
| 4. #21460662 | C2 | semidirect |
| 53. #99×C61 | C8 | semidirect |
| 90. C22⋊C4×C61 | C2×C8 | semidirect |
| 106. C23×C61 | C4⋊C8 | semidirect |
| 119. C2×C4×C61 | C4⋊C8 | semidirect |
| 199. C61 | #8851 | semidirect |
| 224. #99 | #92420 | semidirect |
| 273. C22⋊C4 | C2×#92420 | semidirect |
| 284. C23 | C4⋊#92420 | semidirect |
| 316. C2×C4 | C4⋊#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462666 | 2 |
| #21461792 | 2 |
| #21461762 | 2 |
| #21460662 | 2 |
| #99×Dic61 | 2 |
| #8851 | 61 |