Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 548 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. #23766373 | C2 | semidirect |
| 3. #23761961 | C2 | semidirect |
| 4. #23761896 | C2 | semidirect |
| 5. #23761302 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1478 | C2 | semidirect |
| 11. #19098768 | C4 | semidirect |
| 12. #19098758 | C4 | semidirect |
| 214. #1478 | D79 | semidirect |
| 217. C79 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772864 | 2 |
| #23766373 | 2 |
| #23761961 | 2 |
| #23761896 | 2 |
| #23761302 | 2 |
| #23761259 | 2 |
| C79×#1478 | 2 |
| #9181 | 79 |