Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #23776541 | C2 | semidirect |
| 2. #23775200 | C2 | semidirect |
| 3. #23765650 | C2 | semidirect |
| 4. #23765520 | C2 | semidirect |
| 5. #23765477 | C2 | semidirect |
| 6. #23765359 | C2 | semidirect |
| 7. #23765282 | C2 | semidirect |
| 8. C79×#2170 | C2 | semidirect |
| 9. #19099368 | C22 | semidirect |
| 12. #19099001 | C22 | semidirect |
| 16. C2×D1264 | C22 | semidirect |
| 17. C2×D1264 | C22 | semidirect |
| 18. #19098940 | C22 | semidirect |
| 20. #19098833 | C22 | semidirect |
| 22. #19098681 | C22 | semidirect |
| 23. #19098393 | C22 | semidirect |
| 24. #19098377 | C22 | semidirect |
| 25. #19098371 | C22 | semidirect |
| 26. #504×C79 | C22 | semidirect |
| 28. #364×C79 | C22 | semidirect |
| 29. #350×C79 | C22 | semidirect |
| 30. C4×C16×C79 | C22 | semidirect |
| 45. Dic632 | D4 | semidirect |
| 47. #14579106 | D4 | semidirect |
| 52. D1264 | D4 | semidirect |
| 150. #2170 | D79 | semidirect |
| 151. C79 | #33858 | semidirect |
| 161. #504 | C2×D79 | semidirect |
| 169. #364 | C2×D79 | semidirect |
| 172. #350 | C2×D79 | semidirect |
| 173. C4×C16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776541 | 2 |
| #23775200 | 2 |
| #23765650 | 2 |
| #23765520 | 2 |
| #23765477 | 2 |
| #23765359 | 2 |
| #23765282 | 2 |
| C79×#2170 | 2 |
| #33858 | 79 |