Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19098598 | C2 | semidirect |
| 3. C2×#19098373 | C2 | semidirect |
| 4. #23765010 | C2 | semidirect |
| 5. #23761507 | C2 | semidirect |
| 6. #23761506 | C2 | semidirect |
| 7. C2×#360×C79 | C2 | semidirect |
| 12. #19098801 | C4 | semidirect |
| 13. #19098796 | C4 | semidirect |
| 53. #14579093 | D4 | semidirect |
| 70. #106×C79 | D4 | semidirect |
| 193. C2×#360 | D79 | semidirect |
| 197. C79 | #13002 | semidirect |
| 258. #106 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772977 | 2 |
| C2×#19098598 | 2 |
| C2×#19098373 | 2 |
| #23765010 | 2 |
| #23761507 | 2 |
| #23761506 | 2 |
| C2×#360×C79 | 2 |
| #13002 | 79 |