Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
372 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. #21461366 | C2 | semidirect |
| 2. C2×#16840624 | C2 | semidirect |
| 4. #21460665 | C2 | semidirect |
| 175. C61 | #8607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461366 | 2 |
| C2×#16840624 | 2 |
| #21461114 | 2 |
| #21460665 | 2 |
| #21454459 | 2 |
| #8607 | 61 |