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 |
|---|---|---|
| 1. C2×#19098961 | C2 | semidirect |
| 2. C2×#19098915 | C2 | semidirect |
| 4. #23762999 | C2 | direct (N × H) |
| 5. C2×C8×C79⋊C8 | C2 | semidirect |
| 9. #19098961 | C22 | semidirect |
| 11. #19098915 | C22 | semidirect |
| 18. C8×C79⋊C8 | C22 | semidirect |
| 123. C2×C79 | #1708 | semidirect |
| 132. C79 | C2×#1708 | semidirect |
| 248. C2 | #23762999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098961 | 2 |
| C2×#19098915 | 2 |
| C2×#19098909 | 2 |
| #23762999 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C2×#492×C79 | 2 |
| C2×#1708 | 79 |