Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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 |
|---|---|---|
| 2. C2×#19098920 | C2 | direct (N × H) |
| 3. C22×#14579084 | C2 | semidirect |
| 5. C22×C4×C79⋊C8 | C2 | semidirect |
| 6. C22×#125×C79 | C2 | semidirect |
| 13. #19098920 | C22 | direct (N × H) |
| 14. C2×#14579084 | C22 | semidirect |
| 16. C2×C4×C79⋊C8 | C22 | semidirect |
| 18. C2×#125×C79 | C22 | semidirect |
| 35. #14579084 | C23 | semidirect |
| 37. C4×C79⋊C8 | C23 | semidirect |
| 42. #125×C79 | C23 | semidirect |
| 99. C22×C79 | #488 | semidirect |
| 112. C2×C79 | C2×#488 | semidirect |
| 116. C22×#125 | D79 | semidirect |
| 122. C79 | C22×#488 | semidirect |
| 127. C2×#125 | C2×D79 | semidirect |
| 152. #125 | C22×D79 | semidirect |
| 218. C22 | #19098920 | direct (N × H) |
| 228. C2 | C2×#19098920 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579149 | 2 |
| C2×#19098920 | 2 |
| C22×#14579084 | 2 |
| C22×#14579081 | 2 |
| C22×C4×C79⋊C8 | 2 |
| C22×#125×C79 | 2 |
| C22×#488 | 79 |