Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
650 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23765761 | C2 | semidirect |
| 3. #23764319 | C2 | semidirect |
| 4. #23761909 | C2 | semidirect |
| 5. #23761294 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#1490 | C2 | semidirect |
| 11. #19098853 | C4 | semidirect |
| 12. #19098758 | C4 | semidirect |
| 32. #14579161 | C2×C4 | semidirect |
| 33. #14579158 | C2×C4 | semidirect |
| 46. C4⋊(C79⋊C8) | C2×C4 | semidirect |
| 129. D4×C79 | #104 | semidirect |
| 201. #1490 | D79 | semidirect |
| 204. C79 | #9325 | semidirect |
| 332. D4 | #14579087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773491 | 2 |
| #23765761 | 2 |
| #23764319 | 2 |
| #23761909 | 2 |
| #23761294 | 2 |
| #23761255 | 2 |
| C79×#1490 | 2 |
| #9325 | 79 |