Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #21446602 | C2 | semidirect |
| 5. #21443927 | C2 | semidirect |
| 6. #21443907 | C2 | semidirect |
| 7. C2×C61×#366 | C2 | semidirect |
| 18. #16839570 | C4 | semidirect |
| 46. #14519713 | C2×C4 | semidirect |
| 58. C2×C16×C61 | C2×C4 | semidirect |
| 155. C2×#366 | D61 | semidirect |
| 185. C61 | #12945 | semidirect |
| 210. C2×C16 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454693 | 2 |
| C2×#16839570 | 2 |
| #21447529 | 2 |
| #21446602 | 2 |
| #21443927 | 2 |
| #21443907 | 2 |
| C2×C61×#366 | 2 |
| #12945 | 61 |