Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1004 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #23774338 | C2 | semidirect |
| 3. #23762478 | C2 | semidirect |
| 4. #23762459 | C2 | semidirect |
| 5. #23762062 | C2 | semidirect |
| 6. #23761821 | C2 | semidirect |
| 7. C79×#3550 | C2 | semidirect |
| 19. #19098312 | C22 | semidirect |
| 20. #19098307 | C22 | semidirect |
| 21. Q8⋊(C79⋊C8) | C22 | semidirect |
| 23. #559×C79 | C22 | semidirect |
| 24. Q82×C79 | C22 | semidirect |
| 168. #3550 | D79 | semidirect |
| 175. C79 | #18718 | semidirect |
| 178. #559 | C2×D79 | semidirect |
| 179. Q82 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774338 | 2 |
| #23773853 | 2 |
| #23762478 | 2 |
| #23762459 | 2 |
| #23762062 | 2 |
| #23761821 | 2 |
| C79×#3550 | 2 |
| #18718 | 79 |