Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23763541 | C2 | semidirect |
| 3. #23762168 | C2 | semidirect |
| 6. #23761291 | C2 | semidirect |
| 7. C79×#1302 | C2 | semidirect |
| 171. #1302 | D79 | semidirect |
| 173. C79 | #8917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772572 | 2 |
| #23763541 | 2 |
| #23762168 | 2 |
| #23761986 | 2 |
| #23761866 | 2 |
| #23761291 | 2 |
| C79×#1302 | 2 |
| #8917 | 79 |