Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23763607 | C2 | semidirect |
| 4. #23763582 | C2 | semidirect |
| 6. #23761286 | C2 | semidirect |
| 7. C79×#1282 | C2 | semidirect |
| 24. #19098301 | C4 | semidirect |
| 25. #19098301 | C4 | semidirect |
| 26. #19098298 | C4 | semidirect |
| 27. #19098298 | C4 | semidirect |
| 224. #1282 | D79 | semidirect |
| 225. C79 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772445 | 2 |
| #23763700 | 2 |
| #23763607 | 2 |
| #23763582 | 2 |
| #23761892 | 2 |
| #23761286 | 2 |
| C79×#1282 | 2 |
| #8874 | 79 |