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. #16840689 | C4 | semidirect |
| 15. #16840688 | C4 | semidirect |
| 16. #16840687 | C4 | semidirect |
| 17. #16840686 | C4 | semidirect |
| 23. #16839540 | C4 | semidirect |
| 24. #16839539 | C4 | semidirect |
| 25. #16839539 | C4 | semidirect |
| 26. C61×#347 | C4 | semidirect |
| 91. C16×C61 | C42 | semidirect |
| 93. #11758185 | C42 | semidirect |
| 165. #347 | #6923 | semidirect |
| 168. C61 | #12677 | semidirect |
| 235. C16 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462171 | 2 |
| D61⋊#365 | 2 |
| #21461633 | 2 |
| #21461625 | 2 |
| #21460894 | 2 |
| #21460891 | 2 |
| #347×D61 | 2 |
| #12677 | 61 |