Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 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. C2×#16839563 | C2 | semidirect |
| 4. C2×#16839547 | C2 | semidirect |
| 5. #21445880 | C2 | semidirect |
| 6. #21443916 | C2 | semidirect |
| 7. C2×C61×#361 | C2 | semidirect |
| 64. M32×C61 | D4 | semidirect |
| 179. C2×#361 | D61 | semidirect |
| 210. C61 | #13387 | semidirect |
| 236. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455463 | 2 |
| #21447607 | 2 |
| C2×#16839563 | 2 |
| C2×#16839547 | 2 |
| #21445880 | 2 |
| #21443916 | 2 |
| C2×C61×#361 | 2 |
| #13387 | 61 |