Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16839539 | C2 | semidirect |
| 4. #21446570 | C2 | semidirect |
| 5. #21443925 | C2 | semidirect |
| 6. #21443919 | C2 | semidirect |
| 15. #16839563 | C4 | semidirect |
| 158. C61 | #13155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447535 | 2 |
| C2×#16839539 | 2 |
| #21446696 | 2 |
| #21446570 | 2 |
| #21443925 | 2 |
| #21443919 | 2 |
| C2×C61×#361 | 2 |
| #13155 | 61 |