Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 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. #21445990 | C2 | semidirect |
| 3. #21444500 | C2 | semidirect |
| 6. #21444112 | C2 | semidirect |
| 7. C61×#1549 | C2 | semidirect |
| 147. #1549 | D61 | semidirect |
| 175. C61 | #9774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840110 | 2 |
| #21445990 | 2 |
| #21444500 | 2 |
| #21444488 | 2 |
| #21444486 | 2 |
| #21444112 | 2 |
| C61×#1549 | 2 |
| #9774 | 61 |