Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 958 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×#19098933 | C2 | semidirect |
| 2. C2×#19098922 | C2 | semidirect |
| 3. #23762723 | C2 | direct (N × H) |
| 4. C2×#19098305 | C2 | semidirect |
| 5. C2×#19098303 | C2 | semidirect |
| 9. #19098933 | C22 | semidirect |
| 11. #19098922 | C22 | semidirect |
| 17. #19098305 | C22 | semidirect |
| 18. #19098303 | C22 | semidirect |
| 146. C2×C79 | #1662 | semidirect |
| 155. C79 | C2×#1662 | semidirect |
| 294. C2 | #23762723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098933 | 2 |
| C2×#19098922 | 2 |
| #23762723 | 2 |
| C2×#19098305 | 2 |
| C2×#19098303 | 2 |
| C2×#562×C79 | 2 |
| C2×#1662 | 79 |