Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
732 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23764384 | C2 | semidirect |
| 5. #23761921 | C2 | semidirect |
| 6. #23761285 | C2 | semidirect |
| 7. C79×#1305 | C2 | semidirect |
| 9. C2×#14579194 | C4 | semidirect |
| 16. #19098565 | C4 | semidirect |
| 231. #1305 | D79 | semidirect |
| 233. C79 | #9364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772662 | 2 |
| #23766237 | 2 |
| #23764384 | 2 |
| #23763343 | 2 |
| #23761921 | 2 |
| #23761285 | 2 |
| C79×#1305 | 2 |
| #9364 | 79 |