Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
150 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 25 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. #19098961 | C4 | semidirect |
| 8. C8×C79⋊C8 | C4 | semidirect |
| 64. C79 | #7535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762986 | 2 |
| #23761565 | 2 |
| C79×#1410 | 2 |
| #7535 | 79 |