Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21446804 | C2 | semidirect |
| 3. #21445846 | C2 | semidirect |
| 4. #21445597 | C2 | semidirect |
| 5. #21444390 | C2 | semidirect |
| 8. C22×#11758200 | C4 | semidirect |
| 16. C2×#14519708 | C4 | semidirect |
| 17. C2×#14519700 | C4 | semidirect |
| 18. C2×#14519698 | C4 | semidirect |
| 194. #92418 | #99 | semidirect |
| 262. C61 | #9786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839989 | 2 |
| #21446804 | 2 |
| #21445846 | 2 |
| #21445597 | 2 |
| #21444390 | 2 |
| #21444387 | 2 |
| C61×#1964 | 2 |
| #9786 | 61 |