Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
932 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19098360 | C2 | semidirect |
| 3. C2×#19098359 | C2 | semidirect |
| 4. #23763803 | C2 | semidirect |
| 5. C79×#1888 | C2 | semidirect |
| 8. #19099305 | C4 | semidirect |
| 15. C2×#14579080 | C22 | semidirect |
| 20. #519×C79 | C22 | semidirect |
| 22. C2×#101×C79 | C22 | semidirect |
| 186. #1888 | D79 | semidirect |
| 187. C79 | #12774 | semidirect |
| 197. #519 | C2×D79 | semidirect |
| 201. C2×#101 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099305 | 2 |
| C2×#19098360 | 2 |
| C2×#19098359 | 2 |
| #23763803 | 2 |
| C79×#1888 | 2 |
| #12774 | 79 |