Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
672 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #23765074 | C2 | semidirect |
| 4. #23765055 | C2 | semidirect |
| 5. #23761530 | C2 | semidirect |
| 6. #23761520 | C2 | semidirect |
| 8. C2×#14579191 | C4 | semidirect |
| 9. C22×#11929612 | C4 | semidirect |
| 16. #19098568 | C4 | semidirect |
| 17. #19098559 | C4 | semidirect |
| 31. C22×Dic158 | C2×C4 | semidirect |
| 38. C2×#11929608 | C2×C4 | semidirect |
| 39. C22×C79⋊C8 | C2×C4 | semidirect |
| 50. #14579120 | C2×C4 | semidirect |
| 259. C79 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772677 | 2 |
| #23771861 | 2 |
| #23765074 | 2 |
| #23765055 | 2 |
| #23761530 | 2 |
| #23761520 | 2 |
| C79×#1795 | 2 |
| #13100 | 79 |