Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1870 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 1870 conjugacy classes of subgroups — too many to draw. Only its 248 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. C2×#16840785 | C2 | semidirect |
| 2. #21461347 | C2 | direct (N × H) |
| 3. C2×#16840620 | C2 | semidirect |
| 6. #16840785 | C22 | semidirect |
| 7. C2×#14519844 | C22 | semidirect |
| 10. #16840620 | C22 | semidirect |
| 23. #14519844 | C23 | semidirect |
| 162. C2×C61 | #1555 | semidirect |
| 183. C61 | C2×#1555 | semidirect |
| 322. C2 | #21461347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840785 | 2 |
| #21461347 | 2 |
| C2×#16840620 | 2 |
| C2×#127×D61 | 2 |
| C2×#1555 | 61 |