Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23765188 | C2 | semidirect |
| 4. #23761506 | C2 | semidirect |
| 19. #349×C79 | C4 | semidirect |
| 48. M32×C79 | C2×C4 | semidirect |
| 149. C79 | #12923 | semidirect |
| 162. #349 | Dic79 | semidirect |
| 183. M32 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771990 | 2 |
| #23765188 | 2 |
| #23763433 | 2 |
| #23761506 | 2 |
| C2×#349×C79 | 2 |
| #12923 | 79 |