Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
936 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 936 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×#19099313 | C2 | semidirect |
| 2. #23774586 | C2 | semidirect |
| 3. #23762709 | C2 | semidirect |
| 4. #23762696 | C2 | semidirect |
| 5. #23762024 | C2 | semidirect |
| 6. #23762001 | C2 | semidirect |
| 16. #19098969 | C22 | semidirect |
| 17. #19098927 | C22 | semidirect |
| 22. #19098304 | C22 | semidirect |
| 194. C79 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099313 | 2 |
| #23774586 | 2 |
| #23762709 | 2 |
| #23762696 | 2 |
| #23762024 | 2 |
| #23762001 | 2 |
| C79×#3153 | 2 |
| #18994 | 79 |