Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #21445943 | C2 | semidirect |
| 5. #21443925 | C2 | semidirect |
| 6. #21443918 | C2 | semidirect |
| 7. C61×#2153 | C2 | semidirect |
| 10. #16839875 | C4 | semidirect |
| 11. #16839870 | C4 | semidirect |
| 147. #2153 | D61 | semidirect |
| 175. C61 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454704 | 2 |
| #21447556 | 2 |
| #21447548 | 2 |
| #21445943 | 2 |
| #21443925 | 2 |
| #21443918 | 2 |
| C61×#2153 | 2 |
| #12828 | 61 |