Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 372 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. C2×C4⋊(C79⋊C8) | C4 | semidirect |
| 8. C2×C4×C79⋊C8 | C4 | semidirect |
| 9. #19098289 | C4 | semidirect |
| 36. #99×C79 | C8 | semidirect |
| 150. C79 | #7205 | semidirect |
| 178. #99 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764195 | 2 |
| #23761718 | 2 |
| C4×#99×C79 | 2 |
| #7205 | 79 |