Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1252 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1252 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. #23773850 | C2 | semidirect |
| 3. #23762688 | C2 | semidirect |
| 4. #23761992 | C2 | semidirect |
| 5. #23761991 | C2 | semidirect |
| 6. C79×#3151 | C2 | semidirect |
| 8. #19099305 | C22 | semidirect |
| 16. #19098950 | C22 | semidirect |
| 19. C4×#11929608 | C22 | semidirect |
| 20. #19098303 | C22 | semidirect |
| 21. #19098302 | C22 | semidirect |
| 24. C2×#127×C79 | C22 | semidirect |
| 25. #496×C79 | C22 | semidirect |
| 28. C4×M16×C79 | C22 | semidirect |
| 183. #3151 | D79 | semidirect |
| 187. C79 | #19073 | semidirect |
| 199. C2×#127 | C2×D79 | semidirect |
| 201. #496 | 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 |
| #23773850 | 2 |
| #23762688 | 2 |
| #23761992 | 2 |
| #23761991 | 2 |
| C79×#3151 | 2 |
| #19073 | 79 |