Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
490 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21448101 | C2 | semidirect |
| 3. #21448097 | C2 | semidirect |
| 4. #21448092 | C2 | semidirect |
| 7. C61×#2254 | C2 | semidirect |
| 35. C16×D61 | Q8 | semidirect |
| 100. #2254 | D61 | semidirect |
| 124. C61 | #33726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456330 | 2 |
| #21448101 | 2 |
| #21448097 | 2 |
| #21448092 | 2 |
| #21447602 | 2 |
| C4×C16×D61 | 2 |
| C61×#2254 | 2 |
| #33726 | 61 |