Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16839582 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. C2×#16839575 | C2 | semidirect |
| 5. #21447534 | C2 | semidirect |
| 6. #21445700 | C2 | semidirect |
| 7. C61×#2140 | C2 | semidirect |
| 13. #16840137 | C4 | semidirect |
| 47. #14519713 | D4 | semidirect |
| 64. #107×C61 | D4 | semidirect |
| 172. #2140 | D61 | semidirect |
| 198. C61 | #13261 | semidirect |
| 233. #107 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840137 | 2 |
| C2×#16839582 | 2 |
| C2×#16839576 | 2 |
| C2×#16839575 | 2 |
| #21447534 | 2 |
| #21445700 | 2 |
| C61×#2140 | 2 |
| #13261 | 61 |