Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
13310 conjugacy classes of subgroups; only the 6571 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6571 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 |
|---|---|---|
| 2. C23×#11929607 | C2 | direct (N × H) |
| 3. C24×C79⋊C8 | C2 | semidirect |
| 4. C24×C8×C79 | C2 | semidirect |
| 9. C22×#11929607 | C22 | direct (N × H) |
| 10. C23×C79⋊C8 | C22 | semidirect |
| 12. C23×C8×C79 | C22 | semidirect |
| 18. C2×#11929607 | C23 | direct (N × H) |
| 19. C22×C79⋊C8 | C23 | semidirect |
| 23. C22×C8×C79 | C23 | semidirect |
| 29. #11929607 | C24 | direct (N × H) |
| 30. C2×C79⋊C8 | C24 | semidirect |
| 31. C24×C79 | M16 | semidirect |
| 35. C2×C8×C79 | C24 | semidirect |
| 36. C23×C79 | C2×M16 | semidirect |
| 45. C8×C79 | C25 | semidirect |
| 46. C79⋊C8 | C25 | semidirect |
| 47. C22×C79 | C22×M16 | semidirect |
| 55. C2×C79 | C23×M16 | semidirect |
| 61. C24×C8 | D79 | semidirect |
| 62. C79 | C24×M16 | semidirect |
| 70. C23×C8 | C2×D79 | semidirect |
| 81. C22×C8 | C22×D79 | semidirect |
| 84. C24 | #11929607 | direct (N × H) |
| 93. C2×C8 | C23×D79 | semidirect |
| 96. C23 | C2×#11929607 | direct (N × H) |
| 104. C8 | C24×D79 | semidirect |
| 107. C22 | C22×#11929607 | direct (N × H) |
| 113. C2 | C23×#11929607 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×D79 | 2 |
| C23×#11929607 | 2 |
| C24×C79⋊C8 | 2 |
| C24×C8×C79 | 2 |
| C24×M16 | 79 |