Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
346 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23765568 | C2 | semidirect |
| 3. #23763002 | C2 | semidirect |
| 4. #23761440 | C2 | semidirect |
| 5. #23761373 | C2 | semidirect |
| 6. #23761372 | C2 | semidirect |
| 7. C79×#2230 | C2 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 21. C8×C79⋊C8 | C22 | semidirect |
| 22. #498×C79 | C22 | semidirect |
| 25. #364×C79 | C22 | semidirect |
| 168. #2230 | D79 | semidirect |
| 173. C79 | #12365 | semidirect |
| 176. #498 | C2×D79 | semidirect |
| 189. #364 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775194 | 2 |
| #23765568 | 2 |
| #23763002 | 2 |
| #23761440 | 2 |
| #23761373 | 2 |
| #23761372 | 2 |
| C79×#2230 | 2 |
| #12365 | 79 |