Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 22. #16840160 | C4 | semidirect |
| 25. #16840158 | C4 | semidirect |
| 26. #16840158 | C4 | semidirect |
| 30. C61×#498 | C4 | semidirect |
| 160. C8×C61 | #103 | semidirect |
| 162. #92418 | #103 | semidirect |
| 202. #498 | #6923 | semidirect |
| 218. C61 | #9741 | semidirect |
| 350. C8 | #14519840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461997 | 2 |
| #21461985 | 2 |
| #21461613 | 2 |
| D61⋊#335 | 2 |
| D61⋊#333 | 2 |
| D61⋊#332 | 2 |
| #498×D61 | 2 |
| #9741 | 61 |