Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
738 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23763336 | C2 | semidirect |
| 4. #23761268 | C2 | semidirect |
| 10. #19098483 | C4 | semidirect |
| 11. #19098475 | C4 | semidirect |
| 110. C23×C79 | #103 | semidirect |
| 130. C2×C4×C79 | #103 | semidirect |
| 189. C79 | #9467 | semidirect |
| 294. C23 | #14579086 | semidirect |
| 328. C2×C4 | #14579086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766765 | 2 |
| #23763388 | 2 |
| #23763336 | 2 |
| #23761268 | 2 |
| C79×#2972 | 2 |
| #9467 | 79 |