Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 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. #23765482 | C2 | semidirect |
| 3. #23765481 | C2 | semidirect |
| 4. #23763006 | C2 | semidirect |
| 5. #23761436 | C2 | semidirect |
| 6. #23761374 | C2 | semidirect |
| 7. C79×#1335 | C2 | semidirect |
| 12. #19098943 | C22 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 23. #364×C79 | C22 | semidirect |
| 24. C82×C79 | C22 | semidirect |
| 151. #1335 | D79 | semidirect |
| 152. C79 | #12312 | semidirect |
| 166. #364 | C2×D79 | semidirect |
| 169. C82 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775200 | 2 |
| #23765482 | 2 |
| #23765481 | 2 |
| #23763006 | 2 |
| #23761436 | 2 |
| #23761374 | 2 |
| C79×#1335 | 2 |
| #12312 | 79 |