Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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×#19098913 | C2 | semidirect |
| 4. #23763002 | C2 | direct (N × H) |
| 5. C2×C8×C79⋊C8 | C2 | semidirect |
| 6. C2×#498×C79 | C2 | semidirect |
| 13. #19098913 | C22 | semidirect |
| 19. C8×C79⋊C8 | C22 | semidirect |
| 22. #498×C79 | C22 | semidirect |
| 122. C2×C79 | #1708 | semidirect |
| 126. C2×#498 | D79 | semidirect |
| 132. C79 | C2×#1708 | semidirect |
| 138. #498 | C2×D79 | semidirect |
| 248. C2 | #23763002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098936 | 2 |
| C2×#19098913 | 2 |
| C2×#19098911 | 2 |
| #23763002 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C2×#498×C79 | 2 |
| C2×#1708 | 79 |