Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
63326 conjugacy classes of subgroups; only the 34795 normal subgroups are shown.
This group has 63326 conjugacy classes of subgroups — too many to draw. Only its 34795 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. C24×Dic122 | C2 | semidirect |
| 2. C23×Q8×D61 | C2 | direct (N × H) |
| 4. C24×Q8×C61 | C2 | semidirect |
| 6. C23×Dic122 | C22 | semidirect |
| 7. C22×Q8×D61 | C22 | direct (N × H) |
| 10. C23×Q8×C61 | C22 | semidirect |
| 12. C24×D61 | Q8 | direct (N × H) |
| 14. C22×Dic122 | C23 | semidirect |
| 15. C2×Q8×D61 | C23 | direct (N × H) |
| 19. C22×Q8×C61 | C23 | semidirect |
| 21. C24×C61 | C2×Q8 | semidirect |
| 23. C23×D61 | C2×Q8 | direct (N × H) |
| 25. C2×Q8×C61 | C24 | semidirect |
| 28. Q8×D61 | C24 | direct (N × H) |
| 30. C2×Dic122 | C24 | semidirect |
| 31. C23×C61 | C22×Q8 | semidirect |
| 33. C22×D61 | C22×Q8 | direct (N × H) |
| 35. Q8×C61 | C25 | semidirect |
| 39. Dic122 | C25 | semidirect |
| 41. C22×C61 | C23×Q8 | semidirect |
| 43. C2×D61 | C23×Q8 | direct (N × H) |
| 49. C24×Q8 | D61 | direct (N × H) |
| 51. C2×C61 | C24×Q8 | semidirect |
| 53. D61 | C24×Q8 | direct (N × H) |
| 57. C23×Q8 | C2×D61 | direct (N × H) |
| 61. C61 | C25×Q8 | semidirect |
| 67. C22×Q8 | C22×D61 | direct (N × H) |
| 73. C24 | Q8×D61 | direct (N × H) |
| 77. C2×Q8 | C23×D61 | direct (N × H) |
| 83. C23 | C2×Q8×D61 | direct (N × H) |
| 86. Q8 | C24×D61 | direct (N × H) |
| 92. C22 | C22×Q8×D61 | direct (N × H) |
| 97. C2 | C23×Q8×D61 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic122 | 2 |
| C23×Q8×D61 | 2 |
| C24×C4×D61 | 2 |
| C24×Q8×C61 | 2 |
| C25×Q8 | 61 |