Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 474 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. #23761564 | C2 | direct (N × H) |
| 7. C2×#14579161 | C4 | semidirect |
| 10. #19098935 | C4 | semidirect |
| 13. C2×C4×C79⋊C8 | C4 | semidirect |
| 32. #14579161 | C2×C4 | semidirect |
| 38. C4×C79⋊C8 | C2×C4 | semidirect |
| 165. C2×C79 | #1409 | semidirect |
| 171. C79 | C2×#1409 | semidirect |
| 331. C2 | #23761564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098935 | 2 |
| C2×#19098356 | 2 |
| #23761564 | 2 |
| C2×#353×C79 | 2 |
| C2×#1409 | 79 |