Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
486 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23765121 | C2 | semidirect |
| 4. #23764269 | C2 | semidirect |
| 5. #23761507 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 11. #19099003 | C4 | semidirect |
| 34. C2×Dic316 | C2×C4 | semidirect |
| 46. #14579101 | C2×C4 | semidirect |
| 184. C79 | #13026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099003 | 2 |
| #23772201 | 2 |
| #23765121 | 2 |
| #23764269 | 2 |
| #23761507 | 2 |
| #23761483 | 2 |
| C2×#360×C79 | 2 |
| #13026 | 79 |