Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
770 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 770 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 |
|---|---|---|
| 1. #23771845 | C2 | semidirect |
| 2. #23763318 | C2 | semidirect |
| 3. #23761929 | C2 | semidirect |
| 4. #23761253 | C2 | semidirect |
| 15. C2×#127×C79 | C4 | semidirect |
| 16. C2×#124×C79 | C4 | semidirect |
| 20. #391×C79 | C4 | semidirect |
| 21. #390×C79 | C4 | semidirect |
| 35. C22⋊(C79⋊C8) | D4 | semidirect |
| 252. C79 | #9445 | semidirect |
| 255. C2×#127 | Dic79 | semidirect |
| 256. C2×#124 | Dic79 | semidirect |
| 265. #391 | Dic79 | semidirect |
| 266. #390 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771845 | 2 |
| #23763318 | 2 |
| #23761929 | 2 |
| #23761253 | 2 |
| C79×#2431 | 2 |
| #9445 | 79 |