Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23774059 | C2 | semidirect |
| 3. #23765620 | C2 | semidirect |
| 4. #23765577 | C2 | semidirect |
| 5. #23765482 | C2 | semidirect |
| 7. #23765293 | C2 | semidirect |
| 8. C79×#2166 | C2 | semidirect |
| 13. #19098965 | C22 | semidirect |
| 14. #19098943 | C22 | semidirect |
| 22. #19098671 | C22 | semidirect |
| 26. #19098386 | C22 | semidirect |
| 27. #19098380 | C22 | semidirect |
| 30. #364×C79 | C22 | semidirect |
| 32. #347×C79 | C22 | semidirect |
| 168. #2166 | D79 | semidirect |
| 169. C79 | #33693 | semidirect |
| 189. #364 | C2×D79 | semidirect |
| 193. #347 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774059 | 2 |
| #23772304 | 2 |
| #23765620 | 2 |
| #23765577 | 2 |
| #23765482 | 2 |
| #23765353 | 2 |
| #23765293 | 2 |
| C79×#2166 | 2 |
| #33693 | 79 |