Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19098686 | C2 | semidirect |
| 3. #23765150 | C2 | semidirect |
| 4. #23765129 | C2 | semidirect |
| 5. #23764293 | C2 | semidirect |
| 6. #23761512 | C2 | semidirect |
| 7. C79×#1377 | C2 | semidirect |
| 12. #19099006 | C4 | semidirect |
| 14. #19099001 | C4 | semidirect |
| 188. #1377 | D79 | semidirect |
| 189. C79 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| C2×#19098686 | 2 |
| #23765150 | 2 |
| #23765129 | 2 |
| #23764293 | 2 |
| #23761512 | 2 |
| C79×#1377 | 2 |
| #13024 | 79 |