Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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×#19099279 | C2 | semidirect |
| 2. C2×#19098937 | C2 | semidirect |
| 3. C2×#19098759 | C2 | semidirect |
| 4. #23762484 | C2 | direct (N × H) |
| 5. C2×#19098290 | C2 | semidirect |
| 6. C2×#333×C79 | C2 | semidirect |
| 11. #19099279 | C22 | semidirect |
| 18. #19098937 | C22 | semidirect |
| 20. #19098759 | C22 | semidirect |
| 23. #19098290 | C22 | semidirect |
| 26. #333×C79 | C22 | semidirect |
| 162. C2×C79 | #1624 | semidirect |
| 171. C2×#333 | D79 | semidirect |
| 173. C79 | C2×#1624 | semidirect |
| 192. #333 | C2×D79 | semidirect |
| 330. C2 | #23762484 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099279 | 2 |
| C2×#19098937 | 2 |
| C2×#19098759 | 2 |
| #23762484 | 2 |
| C2×#19098290 | 2 |
| C2×#333×C79 | 2 |
| C2×#1624 | 79 |