Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#16839539 | C2 | semidirect |
| 5. #21445705 | C2 | semidirect |
| 6. #21443935 | C2 | semidirect |
| 7. C61×#1384 | C2 | semidirect |
| 11. #16839873 | C4 | semidirect |
| 12. #16839868 | C4 | semidirect |
| 18. #16839571 | C4 | semidirect |
| 19. #16839570 | C4 | semidirect |
| 42. #14519717 | C2×C4 | semidirect |
| 45. #14519713 | C2×C4 | semidirect |
| 57. C2×C16×C61 | C2×C4 | semidirect |
| 61. #106×C61 | C2×C4 | semidirect |
| 153. #1384 | D61 | semidirect |
| 176. C61 | #12649 | semidirect |
| 201. C2×C16 | C4×D61 | semidirect |
| 207. #106 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454619 | 2 |
| #21447554 | 2 |
| #21447548 | 2 |
| C2×#16839539 | 2 |
| #21445705 | 2 |
| #21443935 | 2 |
| C61×#1384 | 2 |
| #12649 | 61 |