Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#16839591 | C2 | semidirect |
| 3. C2×#16839587 | C2 | semidirect |
| 6. #21443928 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 10. #16840180 | C4 | semidirect |
| 147. #1387 | D61 | semidirect |
| 172. C61 | #12842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840180 | 2 |
| C2×#16839591 | 2 |
| C2×#16839587 | 2 |
| #21445884 | 2 |
| #21445880 | 2 |
| #21443928 | 2 |
| C61×#1387 | 2 |
| #12842 | 61 |