Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21445865 | C2 | semidirect |
| 4. #21443939 | C2 | semidirect |
| 5. C61×#1812 | C2 | semidirect |
| 6. C2×#14519783 | C4 | semidirect |
| 13. #16839785 | C4 | semidirect |
| 15. #16839730 | C4 | semidirect |
| 17. C2×#14519687 | C4 | semidirect |
| 183. #1812 | D61 | semidirect |
| 210. C61 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454535 | 2 |
| #21447482 | 2 |
| #21445865 | 2 |
| #21443939 | 2 |
| C61×#1812 | 2 |
| #12808 | 61 |