Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23774141 | C2 | semidirect |
| 4. #23763063 | C2 | semidirect |
| 5. #23763058 | C2 | semidirect |
| 6. #23763057 | C2 | semidirect |
| 7. #23763013 | C2 | semidirect |
| 8. #23761703 | C2 | semidirect |
| 9. C79×#3185 | C2 | semidirect |
| 12. #19098959 | C22 | semidirect |
| 13. #19098942 | C22 | semidirect |
| 16. #19098915 | C22 | semidirect |
| 17. #19098913 | C22 | semidirect |
| 29. #19098285 | C22 | semidirect |
| 30. #19098284 | C22 | semidirect |
| 31. C8×C79⋊C8 | C22 | semidirect |
| 33. #498×C79 | C22 | semidirect |
| 34. #494×C79 | C22 | semidirect |
| 35. #487×C79 | C22 | semidirect |
| 161. #3185 | D79 | semidirect |
| 169. C79 | #19753 | semidirect |
| 174. #498 | C2×D79 | semidirect |
| 176. #494 | C2×D79 | semidirect |
| 181. #487 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774141 | 2 |
| #23773776 | 2 |
| #23773775 | 2 |
| #23763063 | 2 |
| #23763058 | 2 |
| #23763057 | 2 |
| #23763013 | 2 |
| #23761703 | 2 |
| C79×#3185 | 2 |
| #19753 | 79 |