Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
214 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #23761473 | C2 | semidirect |
| 5. #23761472 | C2 | semidirect |
| 6. #23761471 | C2 | semidirect |
| 7. C79×#1372 | C2 | semidirect |
| 107. #1372 | D79 | semidirect |
| 110. C79 | #12035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765197 | 2 |
| #23762162 | 2 |
| #335×D79 | 2 |
| #23761473 | 2 |
| #23761472 | 2 |
| #23761471 | 2 |
| C79×#1372 | 2 |
| #12035 | 79 |