Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C2×#16840653 | C2 | semidirect |
| 4. #21461628 | C2 | semidirect |
| 5. #21460899 | C2 | semidirect |
| 6. #21460887 | C2 | semidirect |
| 10. #16840803 | C4 | semidirect |
| 11. #16840802 | C4 | semidirect |
| 18. #16840679 | C4 | semidirect |
| 19. #16840678 | C4 | semidirect |
| 25. #16839570 | C4 | semidirect |
| 26. #16839569 | C4 | semidirect |
| 27. #16839568 | C4 | semidirect |
| 28. C61×#359 | C4 | semidirect |
| 39. #14519852 | C2×C4 | semidirect |
| 44. #14519845 | C2×C4 | semidirect |
| 64. C2×#11758185 | C2×C4 | semidirect |
| 65. #14519713 | C2×C4 | semidirect |
| 68. C2×C16×C61 | C2×C4 | semidirect |
| 69. #108×C61 | C2×C4 | semidirect |
| 203. #359 | #6923 | semidirect |
| 206. C61 | #12649 | semidirect |
| 234. C2×C16 | C2×#6923 | semidirect |
| 237. #108 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462573 | 2 |
| #21462139 | 2 |
| C2×#16840653 | 2 |
| #21461628 | 2 |
| #21460899 | 2 |
| #21460887 | 2 |
| #21447545 | 2 |
| #12649 | 61 |