Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. #16840690 | C4 | semidirect |
| 11. C16×#6923 | C4 | semidirect |
| 15. #16839589 | C4 | semidirect |
| 16. #16839588 | C4 | semidirect |
| 17. C61×#366 | C4 | semidirect |
| 114. #366 | #6923 | semidirect |
| 117. C61 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840690 | 2 |
| C2×C16×#6923 | 2 |
| #21461623 | 2 |
| #21460880 | 2 |
| #21447600 | 2 |
| #12670 | 61 |