Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#16839626 | C2 | semidirect |
| 3. #21444090 | C2 | semidirect |
| 4. #21444063 | C2 | semidirect |
| 6. C61×#1446 | C2 | semidirect |
| 9. C2×#14519766 | C4 | semidirect |
| 86. C4×Dic61 | C22⋊C4 | semidirect |
| 150. #1446 | D61 | semidirect |
| 173. C61 | #14662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519766 | 2 |
| C2×#16839626 | 2 |
| #21444090 | 2 |
| #21444063 | 2 |
| #21444059 | 2 |
| C61×#1446 | 2 |
| #14662 | 61 |