Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1066 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #23774405 | C2 | semidirect |
| 3. #23773786 | C2 | semidirect |
| 4. #23762708 | C2 | semidirect |
| 5. #23761999 | C2 | semidirect |
| 6. C79×#1533 | C2 | semidirect |
| 10. #19099120 | C22 | semidirect |
| 16. #19098957 | C22 | semidirect |
| 17. #19098923 | C22 | semidirect |
| 18. #19098922 | C22 | semidirect |
| 25. C4×#11929608 | C22 | semidirect |
| 26. #19098302 | C22 | semidirect |
| 28. #432×C79 | C22 | semidirect |
| 29. #329×C79 | C22 | semidirect |
| 38. #14579161 | C23 | semidirect |
| 64. #14579072 | C23 | semidirect |
| 75. #97×C79 | C23 | semidirect |
| 187. #1533 | D79 | semidirect |
| 189. C79 | #18997 | semidirect |
| 207. #432 | C2×D79 | semidirect |
| 212. #329 | C2×D79 | semidirect |
| 257. #97 | C22×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099305 | 2 |
| #23774405 | 2 |
| #23773786 | 2 |
| #23762708 | 2 |
| #23761999 | 2 |
| C79×#1533 | 2 |
| #18997 | 79 |