Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 414 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. #23762014 | C2 | semidirect |
| 3. #23761965 | C2 | semidirect |
| 5. #23761300 | C2 | semidirect |
| 6. #23761282 | C2 | semidirect |
| 9. #19098973 | C4 | semidirect |
| 10. #19098958 | C4 | semidirect |
| 11. #19098933 | C4 | semidirect |
| 12. #19098922 | C4 | semidirect |
| 206. C79 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774110 | 2 |
| #23762014 | 2 |
| #23761965 | 2 |
| #23761938 | 2 |
| #23761300 | 2 |
| #23761282 | 2 |
| C79×#2968 | 2 |
| #9431 | 79 |