Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. #364×D61 | C2 | semidirect |
| 3. #21443858 | C2 | semidirect |
| 4. #21443855 | C2 | semidirect |
| 5. C61×#1358 | C2 | semidirect |
| 102. #1358 | D61 | semidirect |
| 119. C61 | #11920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456248 | 2 |
| #364×D61 | 2 |
| #21443858 | 2 |
| #21443855 | 2 |
| C61×#1358 | 2 |
| #11920 | 61 |