Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23772441 | C2 | semidirect |
| 3. #23761959 | C2 | semidirect |
| 4. #23761798 | C2 | semidirect |
| 5. #23761297 | C2 | semidirect |
| 6. #23761258 | C2 | semidirect |
| 7. C79×#1804 | C2 | semidirect |
| 11. #19098768 | C4 | semidirect |
| 12. #19098758 | C4 | semidirect |
| 197. #1804 | D79 | semidirect |
| 202. C79 | #9309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772864 | 2 |
| #23772441 | 2 |
| #23761959 | 2 |
| #23761798 | 2 |
| #23761297 | 2 |
| #23761258 | 2 |
| C79×#1804 | 2 |
| #9309 | 79 |