Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 3. #23764997 | C2 | semidirect |
| 5. #23761508 | C2 | semidirect |
| 6. #23761493 | C2 | semidirect |
| 7. C79×#1952 | C2 | semidirect |
| 14. #19098375 | C4 | semidirect |
| 149. #1952 | D79 | semidirect |
| 152. C79 | #13144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098375 | 2 |
| C2×#19098363 | 2 |
| #23764997 | 2 |
| #23764310 | 2 |
| #23761508 | 2 |
| #23761493 | 2 |
| C79×#1952 | 2 |
| #13144 | 79 |