Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 510 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. #23761552 | C2 | direct (N × H) |
| 4. C2×#329×C79 | C2 | semidirect |
| 5. C2×#14579209 | C4 | semidirect |
| 9. #19098735 | C4 | semidirect |
| 12. C2×#14579080 | C4 | semidirect |
| 15. #19098358 | C22 | semidirect |
| 19. #329×C79 | C22 | semidirect |
| 23. #14579209 | C2×C4 | semidirect |
| 38. #14579080 | C2×C4 | semidirect |
| 175. C2×C79 | #1404 | semidirect |
| 180. C2×#329 | D79 | semidirect |
| 182. C79 | C2×#1404 | semidirect |
| 197. #329 | C2×D79 | semidirect |
| 353. C2 | #23761552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098735 | 2 |
| C2×#19098358 | 2 |
| #23761552 | 2 |
| C2×#329×C79 | 2 |
| C2×#1404 | 79 |