Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
634 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21445887 | C2 | semidirect |
| 3. #21443639 | C2 | semidirect |
| 4. C61×#1797 | C2 | semidirect |
| 175. #1797 | D61 | semidirect |
| 201. C61 | #7724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454164 | 2 |
| #21445887 | 2 |
| #21443639 | 2 |
| C61×#1797 | 2 |
| #7724 | 61 |