Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 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. #23774403 | C2 | semidirect |
| 2. #23773786 | C2 | semidirect |
| 3. #23762706 | C2 | semidirect |
| 4. #23762024 | C2 | semidirect |
| 5. #23761998 | C2 | semidirect |
| 7. #19099120 | C22 | semidirect |
| 8. #19098958 | C22 | semidirect |
| 9. #19098922 | C22 | semidirect |
| 10. #19098922 | C22 | semidirect |
| 15. #19098620 | C22 | semidirect |
| 18. C4×#11929608 | C22 | semidirect |
| 19. #19098303 | C22 | semidirect |
| 20. #19098303 | C22 | semidirect |
| 33. #14579161 | C23 | semidirect |
| 44. #14579072 | C23 | semidirect |
| 45. #14579072 | C23 | semidirect |
| 189. C79 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774403 | 2 |
| #23773786 | 2 |
| #23762706 | 2 |
| #23762024 | 2 |
| #23761998 | 2 |
| C2×H(3,𝔽4)×C79 | 2 |
| #18997 | 79 |