Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
220 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #21444729 | C2 | semidirect |
| 3. #21443884 | C2 | semidirect |
| 4. #21443788 | C2 | semidirect |
| 6. #21443740 | C2 | semidirect |
| 125. C61 | #12077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447683 | 2 |
| #21444729 | 2 |
| #21443884 | 2 |
| #21443788 | 2 |
| #21443786 | 2 |
| #21443740 | 2 |
| C61×#1580 | 2 |
| #12077 | 61 |