Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #23765614 | C2 | semidirect |
| 3. #23765174 | C2 | semidirect |
| 4. C2×#19098375 | C2 | semidirect |
| 5. #23765021 | C2 | semidirect |
| 6. C79×#2916 | C2 | semidirect |
| 14. #19098387 | C22 | semidirect |
| 16. #19098345 | C22 | semidirect |
| 20. #430×C79 | C22 | semidirect |
| 132. #2916 | D79 | semidirect |
| 137. C79 | #33657 | semidirect |
| 146. #430 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773048 | 2 |
| #23765614 | 2 |
| #23765174 | 2 |
| C2×#19098375 | 2 |
| #23765021 | 2 |
| C79×#2916 | 2 |
| #33657 | 79 |