Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×#19098995 | C2 | semidirect |
| 2. #23765713 | C2 | direct (N × H) |
| 3. C2×#19098401 | C2 | semidirect |
| 4. C2×#19098398 | C2 | semidirect |
| 5. C2×#19098397 | C2 | semidirect |
| 6. C22×D16×C79 | C2 | semidirect |
| 9. #19098995 | C22 | semidirect |
| 10. C2×Dic632 | C22 | semidirect |
| 12. C2×D1264 | C22 | semidirect |
| 13. #19098401 | C22 | semidirect |
| 14. #19098398 | C22 | semidirect |
| 15. #19098397 | C22 | semidirect |
| 16. C2×C79⋊C32 | C22 | semidirect |
| 21. C2×D16×C79 | C22 | semidirect |
| 30. Dic632 | C23 | semidirect |
| 33. D1264 | C23 | semidirect |
| 34. C79⋊C32 | C23 | semidirect |
| 112. C2×C79 | #2263 | semidirect |
| 116. C22×D16 | D79 | semidirect |
| 121. C79 | C2×#2263 | semidirect |
| 132. C2×D16 | C2×D79 | semidirect |
| 227. C2 | #23765713 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098995 | 2 |
| #23765713 | 2 |
| C2×#19098401 | 2 |
| C2×#19098398 | 2 |
| C2×#19098397 | 2 |
| C22×D16×C79 | 2 |
| C2×#2263 | 79 |