Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #23761950 | C2 | semidirect |
| 4. #23761820 | C2 | semidirect |
| 5. #23761264 | C2 | semidirect |
| 6. #23761262 | C2 | semidirect |
| 9. #19098973 | C4 | semidirect |
| 10. #19098973 | C4 | semidirect |
| 11. #19098922 | C4 | semidirect |
| 12. #19098922 | C4 | semidirect |
| 197. C79 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774636 | 2 |
| #23772387 | 2 |
| #23761950 | 2 |
| #23761820 | 2 |
| #23761264 | 2 |
| #23761262 | 2 |
| C79×#1521 | 2 |
| #9369 | 79 |