Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
640 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23763388 | C2 | semidirect |
| 3. #23761969 | C2 | semidirect |
| 4. #23761280 | C2 | semidirect |
| 5. C79×#2972 | C2 | semidirect |
| 9. #19098493 | C4 | semidirect |
| 10. #19098488 | C4 | semidirect |
| 11. #19098480 | C4 | semidirect |
| 12. #19098472 | C4 | semidirect |
| 63. C22⋊C8×C79 | D4 | semidirect |
| 219. #2972 | D79 | semidirect |
| 224. C79 | #9384 | semidirect |
| 276. C22⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768356 | 2 |
| #23763388 | 2 |
| #23761969 | 2 |
| #23761280 | 2 |
| C79×#2972 | 2 |
| #9384 | 79 |