Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23772317 | C2 | semidirect |
| 3. C2×#19098377 | C2 | semidirect |
| 4. #23764308 | C2 | semidirect |
| 5. #23761503 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 7. C79×#2143 | C2 | semidirect |
| 12. C2×#14579104 | C4 | semidirect |
| 13. C2×#14579102 | C4 | semidirect |
| 174. #2143 | D79 | semidirect |
| 178. C79 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| #23772317 | 2 |
| C2×#19098377 | 2 |
| #23764308 | 2 |
| #23761503 | 2 |
| #23761487 | 2 |
| C79×#2143 | 2 |
| #13036 | 79 |