Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
790 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23765092 | C2 | semidirect |
| 2. #23765072 | C2 | semidirect |
| 3. #23765050 | C2 | semidirect |
| 4. #23763504 | C2 | semidirect |
| 19. #533×C79 | C4 | semidirect |
| 21. C2×#127×C79 | C4 | semidirect |
| 22. #518×C79 | C4 | semidirect |
| 23. #518×C79 | C4 | semidirect |
| 195. C79 | #12722 | semidirect |
| 202. #533 | Dic79 | semidirect |
| 204. C2×#127 | Dic79 | semidirect |
| 205. #518 | Dic79 | semidirect |
| 206. #518 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765092 | 2 |
| #23765072 | 2 |
| #23765050 | 2 |
| #23763504 | 2 |
| C79×#3508 | 2 |
| #12722 | 79 |