Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 462 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×#16839573 | C2 | semidirect |
| 3. C2×#16839572 | C2 | semidirect |
| 4. #21447529 | C2 | semidirect |
| 5. #21446560 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#2139 | C2 | semidirect |
| 59. #14519709 | D4 | semidirect |
| 211. #2139 | D61 | semidirect |
| 242. C61 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456262 | 2 |
| C2×#16839573 | 2 |
| C2×#16839572 | 2 |
| #21447529 | 2 |
| #21446560 | 2 |
| #21443902 | 2 |
| C61×#2139 | 2 |
| #13410 | 61 |