Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 14. #16840687 | C4 | semidirect |
| 15. #16840653 | C4 | semidirect |
| 21. #16839590 | C4 | semidirect |
| 22. #16839589 | C4 | semidirect |
| 23. #16839587 | C4 | semidirect |
| 24. C61×#366 | C4 | semidirect |
| 84. C16×C61 | C42 | semidirect |
| 85. #11758185 | C42 | semidirect |
| 151. #366 | #6923 | semidirect |
| 156. C61 | #12677 | semidirect |
| 217. C16 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840687 | 2 |
| C2×#16840653 | 2 |
| #21461634 | 2 |
| #21461626 | 2 |
| #21460893 | 2 |
| #21460890 | 2 |
| #21447604 | 2 |
| #12677 | 61 |