Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
582 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. #23765647 | C2 | semidirect |
| 4. #23765646 | C2 | semidirect |
| 5. #23765645 | C2 | semidirect |
| 6. #23765644 | C2 | semidirect |
| 9. C79×#2245 | C2 | semidirect |
| 145. D79 | #2245 | direct (N × H) |
| 152. #2245 | D79 | direct (N × H) |
| 155. C79 | C2×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D79 | 2 |
| #494×D79 | 2 |
| #23765647 | 2 |
| #23765646 | 2 |
| #23765645 | 2 |
| #23765644 | 2 |
| #358×D79 | 2 |
| #346×D79 | 2 |
| C79×#2245 | 2 |
| C2×#2245 | 79 |