Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
324 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16839537 | C2 | semidirect |
| 4. #21446565 | C2 | semidirect |
| 5. #21443915 | C2 | semidirect |
| 6. #21443912 | C2 | semidirect |
| 15. #16839566 | C4 | semidirect |
| 16. #16839563 | C4 | semidirect |
| 160. C61 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447526 | 2 |
| C2×#16839537 | 2 |
| #21446708 | 2 |
| #21446565 | 2 |
| #21443915 | 2 |
| #21443912 | 2 |
| C2×C61×#359 | 2 |
| #13152 | 61 |