Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. Q64×D79 | C2 | semidirect |
| 3. #23761616 | C2 | semidirect |
| 4. #23761615 | C2 | semidirect |
| 5. #23761614 | C2 | semidirect |
| 6. C64×D79 | C2 | semidirect |
| 7. C79×SD128 | C2 | semidirect |
| 10. Dic1264 | C22 | semidirect |
| 15. C79⋊C64 | C22 | semidirect |
| 16. Q64×C79 | C22 | semidirect |
| 18. C64×C79 | C22 | semidirect |
| 64. D79 | SD128 | direct (N × H) |
| 70. SD128 | D79 | direct (N × H) |
| 72. C79 | C2×SD128 | semidirect |
| 77. Q64 | C2×D79 | semidirect |
| 83. C64 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q64×D79 | 2 |
| D32×D79 | 2 |
| #23761616 | 2 |
| #23761615 | 2 |
| #23761614 | 2 |
| C64×D79 | 2 |
| C79×SD128 | 2 |
| C2×SD128 | 79 |