Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. #23765189 | C2 | semidirect |
| 3. C2×#19098375 | C2 | semidirect |
| 4. C2×#19098365 | C2 | semidirect |
| 5. C2×#19098346 | C2 | semidirect |
| 6. #23763461 | C2 | semidirect |
| 7. C79×#1382 | C2 | semidirect |
| 49. #14579101 | D4 | semidirect |
| 190. #1382 | D79 | semidirect |
| 191. C79 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773049 | 2 |
| #23765189 | 2 |
| C2×#19098375 | 2 |
| C2×#19098365 | 2 |
| C2×#19098346 | 2 |
| #23763461 | 2 |
| C79×#1382 | 2 |
| #13387 | 79 |