Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23773051 | C2 | semidirect |
| 3. C2×#19098379 | C2 | semidirect |
| 4. #23765116 | C2 | semidirect |
| 5. C2×#19098346 | C2 | semidirect |
| 6. #23761496 | C2 | semidirect |
| 7. C22×SD32×C79 | C2 | semidirect |
| 194. C22×SD32 | D79 | semidirect |
| 201. C79 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098830 | 2 |
| #23773051 | 2 |
| C2×#19098379 | 2 |
| #23765116 | 2 |
| C2×#19098346 | 2 |
| #23761496 | 2 |
| C22×SD32×C79 | 2 |
| #13320 | 79 |