Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
480 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #349×D79 | C2 | semidirect |
| 3. #338×D79 | C2 | semidirect |
| 4. #23761392 | C2 | semidirect |
| 5. #23761391 | C2 | semidirect |
| 6. #23761390 | C2 | semidirect |
| 7. C79×#1341 | C2 | semidirect |
| 20. #19098345 | C22 | semidirect |
| 23. C79⋊#338 | C22 | semidirect |
| 25. #349×C79 | C22 | semidirect |
| 26. #338×C79 | C22 | semidirect |
| 212. D79 | #1341 | direct (N × H) |
| 219. #1341 | D79 | direct (N × H) |
| 220. C79 | C2×#1341 | semidirect |
| 236. #349 | C2×D79 | semidirect |
| 239. #338 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #469×D79 | 2 |
| #349×D79 | 2 |
| #338×D79 | 2 |
| #23761392 | 2 |
| #23761391 | 2 |
| #23761390 | 2 |
| C79×#1341 | 2 |
| C2×#1341 | 79 |