Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #21458972 | C2 | semidirect |
| 2. #21458960 | C2 | semidirect |
| 3. #21448139 | C2 | semidirect |
| 4. #21448134 | C2 | semidirect |
| 5. #21448128 | C2 | semidirect |
| 6. C2×#16839601 | C2 | semidirect |
| 7. C61×#2258 | C2 | semidirect |
| 13. #16840194 | C22 | semidirect |
| 14. C2×Dic488 | C22 | semidirect |
| 16. Dic976 | C22 | semidirect |
| 17. #16839601 | C22 | semidirect |
| 18. #16839601 | C22 | semidirect |
| 19. #16839601 | C22 | semidirect |
| 20. D1952 | C22 | semidirect |
| 22. C61×M64 | C22 | semidirect |
| 23. C2×C32×C61 | C22 | semidirect |
| 98. #2258 | D61 | semidirect |
| 117. M64 | C2×D61 | semidirect |
| 118. C2×C32 | C2×D61 | semidirect |
| 119. C61 | #33983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458972 | 2 |
| #21458960 | 2 |
| #21448139 | 2 |
| #21448134 | 2 |
| #21448128 | 2 |
| C2×#16839601 | 2 |
| C61×#2258 | 2 |
| #33983 | 61 |