Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1136 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 203 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×#19098894 | C2 | semidirect |
| 4. #23762393 | C2 | direct (N × H) |
| 5. C2×#19098301 | C2 | semidirect |
| 18. #19098894 | C22 | semidirect |
| 25. #19098301 | C22 | semidirect |
| 208. C2×C79 | #1608 | semidirect |
| 218. C79 | C2×#1608 | semidirect |
| 419. C2 | #23762393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099189 | 2 |
| C2×#19098894 | 2 |
| C2×#19098488 | 2 |
| #23762393 | 2 |
| C2×#19098301 | 2 |
| C2×#323×C79 | 2 |
| C2×#1608 | 79 |