Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1330 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1330 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×#19098953 | C2 | semidirect |
| 2. #23762689 | C2 | direct (N × H) |
| 3. C2×#19098303 | C2 | semidirect |
| 4. C2×H(3,𝔽4)×C79 | C2 | semidirect |
| 7. C2×#14579158 | C22 | semidirect |
| 9. #19098953 | C22 | semidirect |
| 10. C2×#14579072 | C22 | semidirect |
| 11. #19098303 | C22 | semidirect |
| 13. H(3,𝔽4)×C79 | C22 | semidirect |
| 24. #14579158 | C23 | semidirect |
| 26. #14579072 | C23 | semidirect |
| 105. C2×C79 | #1655 | semidirect |
| 108. C2×H(3,𝔽4) | D79 | semidirect |
| 112. C79 | C2×#1655 | semidirect |
| 116. H(3,𝔽4) | C2×D79 | semidirect |
| 213. C2 | #23762689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098953 | 2 |
| #23762689 | 2 |
| C2×#19098303 | 2 |
| C2×H(3,𝔽4)×C79 | 2 |
| C2×#1655 | 79 |