Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
576 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23762024 | C2 | semidirect |
| 3. #23761907 | C2 | semidirect |
| 4. #23761293 | C2 | semidirect |
| 5. C79×#2372 | C2 | semidirect |
| 9. #19098958 | C4 | semidirect |
| 10. #19098953 | C4 | semidirect |
| 33. #14579161 | C2×C4 | semidirect |
| 34. #14579158 | C2×C4 | semidirect |
| 41. #14579072 | C2×C4 | semidirect |
| 172. #2372 | D79 | semidirect |
| 176. C79 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773864 | 2 |
| #23762024 | 2 |
| #23761907 | 2 |
| #23761293 | 2 |
| C79×#2372 | 2 |
| #9441 | 79 |