Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
348 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23761697 | C2 | semidirect |
| 3. #23761375 | C2 | semidirect |
| 4. #23761372 | C2 | semidirect |
| 5. C79×#2165 | C2 | semidirect |
| 16. #19098284 | C22 | semidirect |
| 17. C8×C79⋊C8 | C22 | semidirect |
| 19. #364×C79 | C22 | semidirect |
| 125. #2165 | D79 | semidirect |
| 129. C79 | #11670 | semidirect |
| 140. #364 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772311 | 2 |
| #23761697 | 2 |
| #23761375 | 2 |
| #23761372 | 2 |
| C79×#2165 | 2 |
| #11670 | 79 |