Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
682 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23764927 | C2 | semidirect |
| 3. #23764805 | C2 | semidirect |
| 4. #23764803 | C2 | semidirect |
| 5. #23761220 | C2 | semidirect |
| 6. #23761220 | C2 | semidirect |
| 7. C79×#1270 | C2 | semidirect |
| 20. #19098433 | C22 | semidirect |
| 23. #19098318 | C22 | semidirect |
| 25. #336×C79 | C22 | semidirect |
| 26. #336×C79 | C22 | semidirect |
| 257. #1270 | D79 | semidirect |
| 258. C79 | #7786 | semidirect |
| 276. #336 | C2×D79 | semidirect |
| 277. #336 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769735 | 2 |
| #23764927 | 2 |
| #23764805 | 2 |
| #23764803 | 2 |
| #23761220 | 2 |
| C79×#1270 | 2 |
| #7786 | 79 |