Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #23764380 | C2 | semidirect |
| 4. #23761965 | C2 | semidirect |
| 5. #23761260 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 10. #19098935 | C4 | semidirect |
| 11. #19098909 | C4 | semidirect |
| 29. #14579161 | C2×C4 | semidirect |
| 30. #14579161 | C2×C4 | semidirect |
| 48. C4×C79⋊C8 | C2×C4 | semidirect |
| 93. C4×Dic79 | SD16 | semidirect |
| 202. C79 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774341 | 2 |
| #23766126 | 2 |
| #23764380 | 2 |
| #23761965 | 2 |
| #23761260 | 2 |
| #23761228 | 2 |
| C79×#1545 | 2 |
| #9295 | 79 |