Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21446640 | C2 | semidirect |
| 4. C2×#16839504 | C2 | semidirect |
| 6. #21443701 | C2 | semidirect |
| 7. C2×C61×#501 | C2 | semidirect |
| 186. C2×#501 | D61 | semidirect |
| 222. C61 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840124 | 2 |
| #21453869 | 2 |
| #21446640 | 2 |
| C2×#16839504 | 2 |
| C2×#16839501 | 2 |
| #21443701 | 2 |
| C2×C61×#501 | 2 |
| #10086 | 61 |