Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 100 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. C2×#16840653 | C2 | semidirect |
| 4. #21461640 | C2 | semidirect |
| 5. #21460896 | C2 | semidirect |
| 6. #21460889 | C2 | semidirect |
| 18. #16840681 | C4 | semidirect |
| 19. #16840680 | C4 | semidirect |
| 25. #16839570 | C4 | semidirect |
| 26. #16839569 | C4 | semidirect |
| 27. #16839568 | C4 | semidirect |
| 28. C61×#359 | C4 | semidirect |
| 200. #359 | #6923 | semidirect |
| 203. C61 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#444 | 2 |
| #21462146 | 2 |
| C2×#16840653 | 2 |
| #21461640 | 2 |
| #21460896 | 2 |
| #21460889 | 2 |
| #21447545 | 2 |
| #12651 | 61 |