Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #21445622 | C2 | semidirect |
| 5. #21445621 | C2 | semidirect |
| 6. #21443948 | C2 | semidirect |
| 7. C61×#1395 | C2 | semidirect |
| 8. C2×#14519785 | C4 | semidirect |
| 15. #16839785 | C4 | semidirect |
| 18. #16839728 | C4 | semidirect |
| 21. C2×#14519687 | C4 | semidirect |
| 22. #16839560 | C4 | semidirect |
| 23. #16839558 | C4 | semidirect |
| 206. #1395 | D61 | semidirect |
| 236. C61 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454534 | 2 |
| #21447502 | 2 |
| #21447482 | 2 |
| #21445622 | 2 |
| #21445621 | 2 |
| #21443948 | 2 |
| C61×#1395 | 2 |
| #12634 | 61 |