Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 3. #23765620 | C2 | direct (N × H) |
| 4. C2×#19098386 | C2 | semidirect |
| 5. C2×#19098380 | C2 | semidirect |
| 18. #19098386 | C22 | semidirect |
| 19. #19098380 | C22 | semidirect |
| 142. C2×C79 | #2239 | semidirect |
| 150. C79 | C2×#2239 | semidirect |
| 285. C2 | #23765620 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098821 | 2 |
| C2×#19098612 | 2 |
| #23765620 | 2 |
| C2×#19098386 | 2 |
| C2×#19098380 | 2 |
| C2×#349×C79 | 2 |
| C2×#2239 | 79 |