Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1152 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1152 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. #23774387 | C2 | semidirect |
| 2. #23773864 | C2 | semidirect |
| 3. #23762706 | C2 | semidirect |
| 4. #23762689 | C2 | semidirect |
| 5. #23762024 | C2 | semidirect |
| 6. #23761998 | C2 | semidirect |
| 7. C2×H(3,𝔽4)×C79 | C2 | semidirect |
| 10. #19099113 | C22 | semidirect |
| 11. #19098958 | C22 | semidirect |
| 12. #19098953 | C22 | semidirect |
| 13. #19098953 | C22 | semidirect |
| 15. #19098922 | C22 | semidirect |
| 19. #19098620 | C22 | semidirect |
| 20. C4×#11929608 | C22 | semidirect |
| 21. #19098303 | C22 | semidirect |
| 22. #19098303 | C22 | semidirect |
| 42. #14579161 | C23 | semidirect |
| 43. #14579158 | C23 | semidirect |
| 51. #14579072 | C23 | semidirect |
| 52. #14579072 | C23 | semidirect |
| 207. C2×H(3,𝔽4) | D79 | semidirect |
| 214. C79 | #18992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774387 | 2 |
| #23773864 | 2 |
| #23762706 | 2 |
| #23762689 | 2 |
| #23762024 | 2 |
| #23761998 | 2 |
| C2×H(3,𝔽4)×C79 | 2 |
| #18992 | 79 |