Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
242 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 102 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. #21460853 | C2 | semidirect |
| 4. #21460852 | C2 | semidirect |
| 5. #21460851 | C2 | semidirect |
| 6. #21460850 | C2 | semidirect |
| 35. #14519716 | C8 | semidirect |
| 64. C16×C61 | C2×C8 | semidirect |
| 66. #11758185 | C2×C8 | semidirect |
| 127. C61 | #12009 | semidirect |
| 171. C16 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461369 | 2 |
| D61⋊#335 | 2 |
| #21460853 | 2 |
| #21460852 | 2 |
| #21460851 | 2 |
| #21460850 | 2 |
| #21447412 | 2 |
| #12009 | 61 |