Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 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. #23765709 | C2 | semidirect |
| 2. #23761615 | C2 | semidirect |
| 3. #23761612 | C2 | semidirect |
| 4. #23761611 | C2 | semidirect |
| 5. C2×D32×C79 | C2 | semidirect |
| 7. Dic1264 | C22 | semidirect |
| 9. D2528 | C22 | semidirect |
| 10. C79⋊C64 | C22 | semidirect |
| 58. C2×D32 | D79 | semidirect |
| 62. C79 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765709 | 2 |
| #23761615 | 2 |
| #23761612 | 2 |
| #23761611 | 2 |
| C2×D32×C79 | 2 |
| #13742 | 79 |