Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23774136 | C2 | semidirect |
| 2. #23772305 | C2 | semidirect |
| 3. #23765613 | C2 | semidirect |
| 4. #23765572 | C2 | semidirect |
| 5. #23765571 | C2 | semidirect |
| 6. #23765473 | C2 | semidirect |
| 7. #23765344 | C2 | semidirect |
| 8. #23765301 | C2 | semidirect |
| 9. #23765299 | C2 | semidirect |
| 10. #23765211 | C2 | semidirect |
| 11. C79×#2213 | C2 | semidirect |
| 16. #19098961 | C22 | semidirect |
| 26. #19098675 | C22 | semidirect |
| 30. #19098387 | C22 | semidirect |
| 31. #19098386 | C22 | semidirect |
| 32. #19098384 | C22 | semidirect |
| 33. #19098376 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 39. #493×C79 | C22 | semidirect |
| 41. #364×C79 | C22 | semidirect |
| 42. #361×C79 | C22 | semidirect |
| 109. Dic316 | #41 | semidirect |
| 114. D632 | #41 | semidirect |
| 142. Q16×C79 | #41 | semidirect |
| 148. D8×C79 | #41 | semidirect |
| 227. #2213 | D79 | semidirect |
| 232. C79 | #33688 | semidirect |
| 239. #493 | C2×D79 | semidirect |
| 257. #364 | C2×D79 | semidirect |
| 259. #361 | C2×D79 | semidirect |
| 336. Q16 | #11929623 | semidirect |
| 347. D8 | #11929623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774136 | 2 |
| #23772305 | 2 |
| #23765613 | 2 |
| #23765572 | 2 |
| #23765571 | 2 |
| #23765473 | 2 |
| #23765344 | 2 |
| #23765301 | 2 |
| #23765299 | 2 |
| #23765211 | 2 |
| C79×#2213 | 2 |
| #33688 | 79 |