Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
13310 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 13310 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×Dic158 | C2 | semidirect |
| 3. C23×#11929613 | C2 | direct (N × H) |
| 4. C24×C8×C79 | C2 | semidirect |
| 7. C23×Dic158 | C22 | semidirect |
| 11. C22×#11929613 | C22 | direct (N × H) |
| 13. C23×C8×C79 | C22 | semidirect |
| 17. C22×Dic158 | C23 | semidirect |
| 21. C2×#11929613 | C23 | direct (N × H) |
| 25. C22×C8×C79 | C23 | semidirect |
| 29. C2×Dic158 | C24 | semidirect |
| 33. #11929613 | C24 | direct (N × H) |
| 34. C24×C79 | SD16 | semidirect |
| 38. C2×C8×C79 | C24 | semidirect |
| 39. C23×C79 | C2×SD16 | semidirect |
| 49. Dic158 | C25 | semidirect |
| 50. C8×C79 | C25 | semidirect |
| 51. C22×C79 | C22×SD16 | semidirect |
| 59. C2×C79 | C23×SD16 | semidirect |
| 65. C24×C8 | D79 | semidirect |
| 66. C79 | C24×SD16 | semidirect |
| 75. C23×C8 | C2×D79 | semidirect |
| 87. C22×C8 | C22×D79 | semidirect |
| 90. C24 | #11929613 | direct (N × H) |
| 100. C2×C8 | C23×D79 | semidirect |
| 103. C23 | C2×#11929613 | direct (N × H) |
| 112. C8 | C24×D79 | semidirect |
| 115. C22 | C22×#11929613 | direct (N × H) |
| 121. C2 | C23×#11929613 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic158 | 2 |
| C24×D316 | 2 |
| C23×#11929613 | 2 |
| C24×C8×C79 | 2 |
| C24×SD16 | 79 |