Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 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 |
|---|---|---|
| 2. C2×#19098972 | C2 | semidirect |
| 4. #23762712 | C2 | direct (N × H) |
| 5. C2×#19098304 | C2 | semidirect |
| 19. #19098972 | C22 | semidirect |
| 25. #19098304 | C22 | semidirect |
| 166. C2×C79 | #1660 | semidirect |
| 175. C79 | C2×#1660 | semidirect |
| 334. C2 | #23762712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099313 | 2 |
| C2×#19098972 | 2 |
| C2×#19098958 | 2 |
| #23762712 | 2 |
| C2×#19098304 | 2 |
| C2×#329×C79 | 2 |
| C2×#1660 | 79 |