Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #21462631 | C2 | semidirect |
| 2. #21461691 | C2 | semidirect |
| 3. #21461199 | C2 | semidirect |
| 4. #21461165 | C2 | semidirect |
| 5. #21460711 | C2 | semidirect |
| 6. #21460653 | C2 | semidirect |
| 27. #16839973 | C4 | semidirect |
| 28. #16839967 | C4 | semidirect |
| 29. #16839959 | C4 | semidirect |
| 32. C61×#459 | C4 | semidirect |
| 245. #459 | #6923 | semidirect |
| 262. C61 | #9210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462631 | 2 |
| #21461691 | 2 |
| #21461199 | 2 |
| #21461165 | 2 |
| #21460711 | 2 |
| #21460653 | 2 |
| #21455267 | 2 |
| #9210 | 61 |