Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
15454 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 15454 conjugacy classes of subgroups — too many to draw. Only its 4427 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×D316 | C2 | semidirect |
| 2. C23×#11929609 | C2 | direct (N × H) |
| 3. C24×C79⋊C8 | C2 | semidirect |
| 4. C24×D4×C79 | C2 | semidirect |
| 7. C23×D316 | C22 | semidirect |
| 8. C22×#11929609 | C22 | direct (N × H) |
| 9. C23×C79⋊C8 | C22 | semidirect |
| 12. C23×D4×C79 | C22 | semidirect |
| 17. C22×D316 | C23 | semidirect |
| 18. C2×#11929609 | C23 | direct (N × H) |
| 19. C22×C79⋊C8 | C23 | semidirect |
| 24. C22×D4×C79 | C23 | semidirect |
| 30. C2×D316 | C24 | semidirect |
| 31. #11929609 | C24 | direct (N × H) |
| 32. C2×C79⋊C8 | C24 | semidirect |
| 35. C24×C79 | D8 | semidirect |
| 38. C2×D4×C79 | C24 | semidirect |
| 43. C23×C79 | C2×D8 | semidirect |
| 48. D4×C79 | C25 | semidirect |
| 52. D316 | C25 | semidirect |
| 53. C79⋊C8 | C25 | semidirect |
| 56. C22×C79 | C22×D8 | semidirect |
| 64. C2×C79 | C23×D8 | semidirect |
| 68. C24×D4 | D79 | semidirect |
| 71. C79 | C24×D8 | semidirect |
| 77. C23×D4 | C2×D79 | semidirect |
| 89. C22×D4 | C22×D79 | semidirect |
| 98. C24 | #11929609 | direct (N × H) |
| 103. C2×D4 | C23×D79 | semidirect |
| 112. C23 | C2×#11929609 | direct (N × H) |
| 117. D4 | C24×D79 | semidirect |
| 125. C22 | C22×#11929609 | direct (N × H) |
| 131. C2 | C23×#11929609 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D316 | 2 |
| C23×#11929609 | 2 |
| C24×C79⋊C8 | 2 |
| C24×D4×C79 | 2 |
| C24×D8 | 79 |