Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
488 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 12. C22×C4⋊C4×C79 | C4 | semidirect |
| 17. #385×C79 | C4 | semidirect |
| 19. #380×C79 | C4 | semidirect |
| 168. C79 | #13295 | semidirect |
| 170. C22×C4⋊C4 | Dic79 | semidirect |
| 178. #385 | Dic79 | semidirect |
| 180. #380 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763392 | 2 |
| C4×#14579076 | 2 |
| #23761518 | 2 |
| C79×#2487 | 2 |
| #13295 | 79 |