Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
402 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #23761561 | C2 | semidirect |
| 5. #23761560 | C2 | semidirect |
| 6. #23761559 | C2 | semidirect |
| 7. C79×#1407 | C2 | semidirect |
| 11. C4⋊Q8×D79 | C4 | semidirect |
| 13. #19098957 | C4 | semidirect |
| 14. #19098955 | C4 | semidirect |
| 19. #19098515 | C4 | semidirect |
| 187. #1407 | D79 | semidirect |
| 188. C79 | #13580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773856 | 2 |
| #23765082 | 2 |
| #23765064 | 2 |
| #23761561 | 2 |
| #23761560 | 2 |
| #23761559 | 2 |
| C79×#1407 | 2 |
| #13580 | 79 |