Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
468 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19098358 | C2 | semidirect |
| 3. #23761558 | C2 | direct (N × H) |
| 4. C2×#355×C79 | C2 | semidirect |
| 7. C2×#14579158 | C4 | semidirect |
| 10. #19098953 | C4 | semidirect |
| 13. C2×#14579072 | C4 | semidirect |
| 15. #19098358 | C22 | semidirect |
| 19. #355×C79 | C22 | semidirect |
| 33. #14579158 | C2×C4 | semidirect |
| 38. #14579072 | C2×C4 | semidirect |
| 158. C2×C79 | #1406 | semidirect |
| 162. C2×#355 | D79 | semidirect |
| 165. C79 | C2×#1406 | semidirect |
| 178. #355 | C2×D79 | semidirect |
| 319. C2 | #23761558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098953 | 2 |
| C2×#19098358 | 2 |
| #23761558 | 2 |
| C2×#355×C79 | 2 |
| C2×#1406 | 79 |