Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763438 | C2 | semidirect |
| 4. #23761276 | C2 | semidirect |
| 5. C79×#1810 | C2 | semidirect |
| 189. #1810 | D79 | semidirect |
| 192. C79 | #8613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098634 | 2 |
| #23763438 | 2 |
| #23761736 | 2 |
| #23761276 | 2 |
| C79×#1810 | 2 |
| #8613 | 79 |