Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19098358 | C2 | semidirect |
| 3. #23761561 | C2 | semidirect |
| 4. #23761558 | C2 | semidirect |
| 5. C2×#355×C79 | C2 | semidirect |
| 8. #19099113 | C4 | semidirect |
| 9. #19098958 | C4 | semidirect |
| 11. #19098953 | C4 | semidirect |
| 16. C4×#11929608 | C4 | semidirect |
| 37. #14579161 | C2×C4 | semidirect |
| 38. #14579158 | C2×C4 | semidirect |
| 45. #14579072 | C2×C4 | semidirect |
| 46. #14579072 | C2×C4 | semidirect |
| 178. C2×#355 | D79 | semidirect |
| 182. C79 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773864 | 2 |
| C2×#19098358 | 2 |
| #23761561 | 2 |
| #23761558 | 2 |
| C2×#355×C79 | 2 |
| #13578 | 79 |