Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19098685 | C2 | semidirect |
| 3. #23765129 | C2 | semidirect |
| 4. #23764291 | C2 | semidirect |
| 5. #23761513 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 7. C79×#2148 | C2 | semidirect |
| 11. #19099003 | C4 | semidirect |
| 13. #19098998 | C4 | semidirect |
| 184. #2148 | 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 |
|---|---|
| #23776534 | 2 |
| C2×#19098685 | 2 |
| #23765129 | 2 |
| #23764291 | 2 |
| #23761513 | 2 |
| #23761483 | 2 |
| C79×#2148 | 2 |
| #13024 | 79 |