Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1132 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23777805 | C2 | semidirect |
| 2. #23774318 | C2 | semidirect |
| 3. #23762481 | C2 | semidirect |
| 4. #23762452 | C2 | semidirect |
| 5. #23762062 | C2 | semidirect |
| 6. #23761818 | C2 | semidirect |
| 7. C79×#3151 | C2 | semidirect |
| 9. #19099279 | C22 | semidirect |
| 12. #19099198 | C22 | semidirect |
| 18. #19098755 | C22 | semidirect |
| 20. #19098616 | C22 | semidirect |
| 21. #19098312 | C22 | semidirect |
| 22. #19098307 | C22 | semidirect |
| 23. #19098292 | C22 | semidirect |
| 26. C2×#127×C79 | C22 | semidirect |
| 29. #492×C79 | C22 | semidirect |
| 30. C4×M16×C79 | C22 | semidirect |
| 182. #3151 | D79 | semidirect |
| 187. C79 | #18714 | semidirect |
| 198. C2×#127 | C2×D79 | semidirect |
| 202. #492 | C2×D79 | semidirect |
| 207. C4×M16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23774318 | 2 |
| #23762481 | 2 |
| #23762452 | 2 |
| #23762062 | 2 |
| #23761818 | 2 |
| C79×#3151 | 2 |
| #18714 | 79 |