Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #23772467 | C2 | semidirect |
| 2. #23765065 | C2 | semidirect |
| 3. #23763364 | C2 | semidirect |
| 4. #23761530 | C2 | semidirect |
| 19. #456×C79 | C4 | semidirect |
| 21. #454×C79 | C4 | semidirect |
| 200. C79 | #13054 | semidirect |
| 204. #456 | Dic79 | semidirect |
| 206. #454 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772467 | 2 |
| #23765065 | 2 |
| #23763364 | 2 |
| #23761530 | 2 |
| C79×#3018 | 2 |
| #13054 | 79 |