Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
266 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 19. #16839537 | C4 | semidirect |
| 20. C4×#11758185 | C4 | semidirect |
| 21. C16×Dic61 | C4 | semidirect |
| 22. C61×#346 | C4 | semidirect |
| 123. #346 | #6923 | semidirect |
| 128. C61 | #12911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#368 | 2 |
| #21462170 | 2 |
| #21462166 | 2 |
| #21461738 | 2 |
| #21447417 | 2 |
| #12911 | 61 |