Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23761421 | C2 | semidirect |
| 4. #23761400 | C2 | semidirect |
| 12. C2×C22⋊Q8×C79 | C4 | semidirect |
| 14. #398×C79 | C4 | semidirect |
| 17. #395×C79 | C4 | semidirect |
| 22. #381×C79 | C4 | semidirect |
| 189. C79 | #11826 | semidirect |
| 190. C2×C22⋊Q8 | Dic79 | semidirect |
| 194. #398 | Dic79 | semidirect |
| 197. #395 | Dic79 | semidirect |
| 202. #381 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763388 | 2 |
| #23761741 | 2 |
| #23761421 | 2 |
| #23761400 | 2 |
| C79×#2638 | 2 |
| #11826 | 79 |