Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21447607 | C2 | semidirect |
| 3. #21447531 | C2 | semidirect |
| 4. C2×#16839543 | C2 | semidirect |
| 5. #21445849 | C2 | semidirect |
| 6. #21443926 | C2 | semidirect |
| 7. C2×C61×#360 | C2 | semidirect |
| 72. M32×C61 | D4 | semidirect |
| 203. C2×#360 | D61 | semidirect |
| 236. C61 | #13386 | semidirect |
| 269. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455424 | 2 |
| #21447607 | 2 |
| #21447531 | 2 |
| C2×#16839543 | 2 |
| #21445849 | 2 |
| #21443926 | 2 |
| C2×C61×#360 | 2 |
| #13386 | 61 |