Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 12. #19098285 | C4 | semidirect |
| 13. #19098285 | C4 | semidirect |
| 14. #19098284 | C4 | semidirect |
| 15. C8×C79⋊C8 | C4 | semidirect |
| 109. C79 | #8804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761703 | 2 |
| #23761273 | 2 |
| #23761272 | 2 |
| #23761271 | 2 |
| #23761264 | 2 |
| C79×#1288 | 2 |
| #8804 | 79 |