Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23772311 | C2 | semidirect |
| 2. #23765612 | C2 | semidirect |
| 3. #23765568 | C2 | semidirect |
| 4. #23765473 | C2 | semidirect |
| 5. #23765345 | C2 | semidirect |
| 6. #23765296 | C2 | semidirect |
| 7. #23765212 | C2 | semidirect |
| 8. C79×#3184 | C2 | semidirect |
| 18. #19098385 | C22 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 20. #19098376 | C22 | semidirect |
| 23. #19098341 | C22 | semidirect |
| 25. #498×C79 | C22 | semidirect |
| 26. #493×C79 | C22 | semidirect |
| 31. #442×C79 | C22 | semidirect |
| 80. Dic316 | #41 | semidirect |
| 84. D632 | #41 | semidirect |
| 170. #3184 | D79 | semidirect |
| 178. C79 | #33688 | semidirect |
| 183. #498 | C2×D79 | semidirect |
| 184. #493 | C2×D79 | semidirect |
| 193. #442 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772311 | 2 |
| #23765612 | 2 |
| #23765568 | 2 |
| #23765473 | 2 |
| #23765345 | 2 |
| #23765296 | 2 |
| #23765212 | 2 |
| C79×#3184 | 2 |
| #33688 | 79 |