Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765258 | C2 | semidirect |
| 4. #23761580 | C2 | semidirect |
| 6. C32×Dic79 | C2 | semidirect |
| 7. C79×#1424 | C2 | semidirect |
| 12. #19098402 | C4 | semidirect |
| 25. Dic632 | C2×C4 | semidirect |
| 36. C32×C79 | C2×C4 | semidirect |
| 80. Dic79 | SD64 | semidirect |
| 89. #1424 | D79 | semidirect |
| 93. C79 | C4×SD64 | semidirect |
| 122. C32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098402 | 2 |
| #23765258 | 2 |
| #23765246 | 2 |
| #23761580 | 2 |
| #23761577 | 2 |
| C32×Dic79 | 2 |
| C79×#1424 | 2 |
| C4×SD64 | 79 |