Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1150 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 187 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×#19098958 | C2 | semidirect |
| 2. C2×#19098922 | C2 | semidirect |
| 3. #23762706 | C2 | direct (N × H) |
| 4. C2×#19098303 | C2 | semidirect |
| 5. C2×#19098303 | C2 | semidirect |
| 9. C2×#14579161 | C22 | semidirect |
| 11. #19098958 | C22 | semidirect |
| 13. #19098922 | C22 | semidirect |
| 16. C2×#14579072 | C22 | semidirect |
| 17. C2×#14579072 | C22 | semidirect |
| 18. #19098303 | C22 | semidirect |
| 19. #19098303 | C22 | semidirect |
| 38. #14579161 | C23 | semidirect |
| 44. #14579072 | C23 | semidirect |
| 45. #14579072 | C23 | semidirect |
| 184. C2×C79 | #1659 | semidirect |
| 193. C79 | C2×#1659 | semidirect |
| 370. C2 | #23762706 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098958 | 2 |
| C2×#19098922 | 2 |
| #23762706 | 2 |
| C2×#19098303 | 2 |
| C2×H(3,𝔽4)×C79 | 2 |
| C2×#1659 | 79 |