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. #23764380 | C2 | semidirect |
| 4. #23761872 | C2 | semidirect |
| 5. #23761292 | C2 | semidirect |
| 6. #23761289 | C2 | semidirect |
| 9. #19098973 | C4 | semidirect |
| 10. #19098958 | C4 | semidirect |
| 11. #19098933 | C4 | semidirect |
| 12. #19098922 | C4 | semidirect |
| 206. C79 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774007 | 2 |
| #23764380 | 2 |
| #23761886 | 2 |
| #23761872 | 2 |
| #23761292 | 2 |
| #23761289 | 2 |
| C79×#2995 | 2 |
| #8998 | 79 |