Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
936 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23774590 | C2 | semidirect |
| 3. #23762711 | C2 | semidirect |
| 4. #23762698 | C2 | semidirect |
| 5. #23762024 | C2 | semidirect |
| 6. #23762002 | C2 | semidirect |
| 7. C2×#563×C79 | C2 | semidirect |
| 11. #19098973 | C22 | semidirect |
| 15. #19098929 | C22 | semidirect |
| 21. #19098305 | C22 | semidirect |
| 187. C2×#563 | D79 | semidirect |
| 194. C79 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774590 | 2 |
| #23773864 | 2 |
| #23762711 | 2 |
| #23762698 | 2 |
| #23762024 | 2 |
| #23762002 | 2 |
| C2×#563×C79 | 2 |
| #18994 | 79 |