Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23776538 | C2 | semidirect |
| 2. #23775200 | C2 | semidirect |
| 3. #23765650 | C2 | semidirect |
| 4. #23765521 | C2 | semidirect |
| 5. #23765476 | C2 | semidirect |
| 6. #23765358 | C2 | semidirect |
| 7. #23765238 | C2 | semidirect |
| 8. C79×#2178 | C2 | semidirect |
| 10. #19099365 | C22 | semidirect |
| 12. #19098998 | C22 | semidirect |
| 14. C2×D1264 | C22 | semidirect |
| 15. C2×D1264 | C22 | semidirect |
| 17. #19098979 | C22 | semidirect |
| 18. #19098940 | C22 | semidirect |
| 19. #19098834 | C22 | semidirect |
| 23. #19098384 | C22 | semidirect |
| 24. #19098375 | C22 | semidirect |
| 25. #19098346 | C22 | semidirect |
| 27. #443×C79 | C22 | semidirect |
| 28. #368×C79 | C22 | semidirect |
| 29. #359×C79 | C22 | semidirect |
| 30. C4×C16×C79 | C22 | semidirect |
| 58. Q32×C79 | D4 | semidirect |
| 59. SD32×C79 | D4 | semidirect |
| 60. D16×C79 | D4 | semidirect |
| 149. #2178 | D79 | semidirect |
| 151. C79 | #33858 | semidirect |
| 167. #443 | C2×D79 | semidirect |
| 168. #368 | C2×D79 | semidirect |
| 171. #359 | C2×D79 | semidirect |
| 173. C4×C16 | C2×D79 | semidirect |
| 190. Q32 | D316 | semidirect |
| 192. SD32 | D316 | semidirect |
| 197. D16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776538 | 2 |
| #23775200 | 2 |
| #23765650 | 2 |
| #23765521 | 2 |
| #23765476 | 2 |
| #23765358 | 2 |
| #23765238 | 2 |
| C79×#2178 | 2 |
| #33858 | 79 |