Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21443983 | C2 | semidirect |
| 7. C2×#14519777 | C4 | semidirect |
| 10. #16840141 | C4 | semidirect |
| 13. C4×#11758194 | C4 | semidirect |
| 169. C61 | #13586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456279 | 2 |
| #21447484 | 2 |
| #21443983 | 2 |
| C61×#2126 | 2 |
| #13586 | 61 |