Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23765861 | C2 | semidirect |
| 3. #23764229 | C2 | semidirect |
| 4. #23761826 | C2 | semidirect |
| 5. #23761303 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1502 | C2 | semidirect |
| 11. #19098840 | C4 | semidirect |
| 12. #19098755 | C4 | semidirect |
| 104. C4×Dic79 | D8 | semidirect |
| 220. #1502 | D79 | semidirect |
| 224. C79 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773396 | 2 |
| #23765861 | 2 |
| #23764229 | 2 |
| #23761826 | 2 |
| #23761303 | 2 |
| #23761232 | 2 |
| C79×#1502 | 2 |
| #9237 | 79 |