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. #23774139 | C2 | semidirect |
| 2. #23772305 | C2 | semidirect |
| 3. #23765616 | C2 | semidirect |
| 4. #23765568 | C2 | semidirect |
| 5. #23765477 | C2 | semidirect |
| 6. #23765476 | C2 | semidirect |
| 7. #23765347 | C2 | semidirect |
| 8. #23765297 | C2 | semidirect |
| 9. #23765295 | C2 | semidirect |
| 10. #23765211 | C2 | semidirect |
| 11. C79×#2230 | C2 | semidirect |
| 17. #19098940 | C22 | semidirect |
| 27. #19098674 | C22 | semidirect |
| 31. #19098385 | C22 | semidirect |
| 32. #19098384 | C22 | semidirect |
| 33. #19098377 | C22 | semidirect |
| 34. #19098375 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 38. #498×C79 | C22 | semidirect |
| 40. #365×C79 | C22 | semidirect |
| 41. #364×C79 | C22 | semidirect |
| 111. Dic316 | #41 | semidirect |
| 120. D632 | #41 | semidirect |
| 144. Q16×C79 | #41 | semidirect |
| 146. D8×C79 | #41 | semidirect |
| 225. #2230 | D79 | semidirect |
| 232. C79 | #33688 | semidirect |
| 238. #498 | C2×D79 | semidirect |
| 255. #365 | C2×D79 | semidirect |
| 257. #364 | C2×D79 | semidirect |
| 336. Q16 | #11929625 | semidirect |
| 347. D8 | #11929625 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774139 | 2 |
| #23772305 | 2 |
| #23765616 | 2 |
| #23765568 | 2 |
| #23765477 | 2 |
| #23765476 | 2 |
| #23765347 | 2 |
| #23765297 | 2 |
| #23765295 | 2 |
| #23765211 | 2 |
| C79×#2230 | 2 |
| #33688 | 79 |