Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23769198 | C2 | semidirect |
| 4. #23763497 | C2 | semidirect |
| 5. #23761920 | C2 | semidirect |
| 6. #23761305 | C2 | semidirect |
| 230. C79 | #9933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773336 | 2 |
| #23769198 | 2 |
| #23764237 | 2 |
| #23763497 | 2 |
| #23761920 | 2 |
| #23761305 | 2 |
| C79×#3193 | 2 |
| #9933 | 79 |