Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23765197 | C2 | semidirect |
| 3. #23762162 | C2 | semidirect |
| 4. #23761362 | C2 | semidirect |
| 5. #23761361 | C2 | semidirect |
| 6. #23761360 | C2 | semidirect |
| 7. C79×#1331 | C2 | semidirect |
| 21. C4×C79⋊C16 | C22 | semidirect |
| 22. #19098316 | C22 | semidirect |
| 25. C4×C16×C79 | C22 | semidirect |
| 26. #335×C79 | C22 | semidirect |
| 177. #1331 | D79 | semidirect |
| 178. C79 | #11661 | semidirect |
| 194. C4×C16 | C2×D79 | semidirect |
| 196. #335 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D79 | 2 |
| #23765197 | 2 |
| #23762162 | 2 |
| #23761362 | 2 |
| #23761361 | 2 |
| #23761360 | 2 |
| C79×#1331 | 2 |
| #11661 | 79 |