Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 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×#16840179 | C2 | semidirect |
| 3. #21447546 | C2 | semidirect |
| 4. C2×#16839568 | C2 | semidirect |
| 5. C61×#2916 | C2 | semidirect |
| 13. C2×#14519717 | C22 | semidirect |
| 14. C22×#11758185 | C22 | semidirect |
| 15. #16839568 | C22 | semidirect |
| 16. #16839568 | C22 | semidirect |
| 20. C2×#108×C61 | C22 | semidirect |
| 115. #2916 | D61 | semidirect |
| 134. C2×#108 | C2×D61 | semidirect |
| 137. C61 | #33385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460593 | 2 |
| C2×#16840179 | 2 |
| #21447546 | 2 |
| C2×#16839568 | 2 |
| C61×#2916 | 2 |
| #33385 | 61 |