Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. C23×C79⋊C8 | C4 | semidirect |
| 7. C2×C22⋊(C79⋊C8) | C4 | semidirect |
| 10. #19098287 | C4 | semidirect |
| 36. #99×C79 | C8 | semidirect |
| 152. C79 | #7204 | semidirect |
| 181. #99 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763693 | 2 |
| #23761721 | 2 |
| C4×#99×C79 | 2 |
| #7204 | 79 |