Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23765614 | C2 | semidirect |
| 3. #23761390 | C2 | semidirect |
| 4. #23761336 | C2 | semidirect |
| 5. C79×#2091 | C2 | semidirect |
| 13. #19098345 | C22 | semidirect |
| 15. #430×C79 | C22 | semidirect |
| 18. #338×C79 | C22 | semidirect |
| 129. #2091 | D79 | semidirect |
| 132. C79 | #12298 | semidirect |
| 139. #430 | C2×D79 | semidirect |
| 145. #338 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774200 | 2 |
| #23765614 | 2 |
| #23761390 | 2 |
| #23761336 | 2 |
| C79×#2091 | 2 |
| #12298 | 79 |