Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
500 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21445815 | C2 | semidirect |
| 4. #21443945 | C2 | semidirect |
| 5. C61×#1801 | C2 | semidirect |
| 189. C4×C61 | #355 | semidirect |
| 196. #1801 | D61 | semidirect |
| 222. C61 | #12801 | semidirect |
| 390. C4 | #16839558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519766 | 2 |
| C2×#16839558 | 2 |
| #21445815 | 2 |
| #21443945 | 2 |
| C61×#1801 | 2 |
| #12801 | 61 |