Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23764353 | C2 | semidirect |
| 5. #23761269 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1558 | C2 | semidirect |
| 9. #19098969 | C4 | semidirect |
| 10. #19098925 | C4 | semidirect |
| 192. #1558 | D79 | semidirect |
| 196. C79 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774621 | 2 |
| #23772541 | 2 |
| #23764353 | 2 |
| #23761926 | 2 |
| #23761269 | 2 |
| #23761257 | 2 |
| C79×#1558 | 2 |
| #9375 | 79 |