Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 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. C2×#16839570 | C2 | semidirect |
| 3. #21447529 | C2 | semidirect |
| 4. C2×#16839545 | C2 | semidirect |
| 5. #21445884 | C2 | semidirect |
| 6. #21443927 | C2 | semidirect |
| 7. C2×C61×#366 | C2 | semidirect |
| 63. C2×C16×C61 | D4 | semidirect |
| 178. C2×#366 | D61 | semidirect |
| 210. C61 | #13384 | semidirect |
| 241. C2×C16 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455491 | 2 |
| C2×#16839570 | 2 |
| #21447529 | 2 |
| C2×#16839545 | 2 |
| #21445884 | 2 |
| #21443927 | 2 |
| C2×C61×#366 | 2 |
| #13384 | 61 |