Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
340 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #23761576 | C2 | direct (N × H) |
| 5. C2×#14579153 | C4 | semidirect |
| 8. #19098917 | C4 | semidirect |
| 13. C2×C4×C79⋊C8 | C4 | semidirect |
| 23. #14579153 | C2×C4 | semidirect |
| 34. C4×C79⋊C8 | C2×C4 | semidirect |
| 134. C2×C79 | #1414 | semidirect |
| 140. C79 | C2×#1414 | semidirect |
| 269. C2 | #23761576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098917 | 2 |
| C2×#19098358 | 2 |
| #23761576 | 2 |
| C2×#355×C79 | 2 |
| C2×#1414 | 79 |