Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23765009 | C2 | semidirect |
| 3. #23763437 | C2 | semidirect |
| 4. #23761416 | C2 | semidirect |
| 5. #23761415 | C2 | semidirect |
| 6. #23761414 | C2 | semidirect |
| 7. C79×#1349 | C2 | semidirect |
| 21. C22⋊(C79⋊C16) | C22 | semidirect |
| 23. #19098328 | C22 | semidirect |
| 25. C22⋊C16×C79 | C22 | semidirect |
| 26. #341×C79 | C22 | semidirect |
| 195. #1349 | D79 | semidirect |
| 196. C79 | #11895 | semidirect |
| 213. C22⋊C16 | C2×D79 | semidirect |
| 215. #341 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D79 | 2 |
| #23765009 | 2 |
| #23763437 | 2 |
| #23761416 | 2 |
| #23761415 | 2 |
| #23761414 | 2 |
| C79×#1349 | 2 |
| #11895 | 79 |