Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23763203 | C2 | semidirect |
| 4. #23761530 | C2 | semidirect |
| 6. C2×#14579168 | C4 | semidirect |
| 10. #19098587 | C4 | semidirect |
| 12. #19098530 | C4 | semidirect |
| 15. C2×C4×C79⋊C8 | C4 | semidirect |
| 21. #356×C79 | C4 | semidirect |
| 22. #355×C79 | C4 | semidirect |
| 157. C79 | #12633 | semidirect |
| 170. #356 | Dic79 | semidirect |
| 171. #355 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772112 | 2 |
| #23765065 | 2 |
| #23763203 | 2 |
| #23761530 | 2 |
| C79×#2132 | 2 |
| #12633 | 79 |