Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765065 | C2 | semidirect |
| 3. #23761558 | C2 | semidirect |
| 4. C79×#2132 | C2 | semidirect |
| 7. C2×#14579158 | C4 | semidirect |
| 8. #19098953 | C4 | semidirect |
| 13. C4×#11929608 | C4 | semidirect |
| 14. #19098358 | C22 | semidirect |
| 19. #355×C79 | C22 | semidirect |
| 158. #2132 | D79 | semidirect |
| 161. C79 | #13579 | semidirect |
| 174. #355 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773853 | 2 |
| #23765065 | 2 |
| #23761558 | 2 |
| C79×#2132 | 2 |
| #13579 | 79 |