Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1722 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 1. C2×#19098935 | C2 | semidirect |
| 2. C2×#19098853 | C2 | semidirect |
| 3. #23762516 | C2 | direct (N × H) |
| 4. C2×#19098307 | C2 | semidirect |
| 5. C2×D4⋊(C79⋊C8) | C2 | semidirect |
| 8. C2×#14579161 | C22 | semidirect |
| 10. #19098935 | C22 | semidirect |
| 12. #19098853 | C22 | semidirect |
| 14. C2×C4⋊(C79⋊C8) | C22 | semidirect |
| 16. C2×C4×C79⋊C8 | C22 | semidirect |
| 17. #19098307 | C22 | semidirect |
| 18. D4⋊(C79⋊C8) | C22 | semidirect |
| 34. #14579161 | C23 | semidirect |
| 38. C4⋊(C79⋊C8) | C23 | semidirect |
| 41. C4×C79⋊C8 | C23 | semidirect |
| 96. C2×D4×C79 | SD16 | semidirect |
| 133. D4×C79 | C2×SD16 | semidirect |
| 173. C2×C79 | #1629 | semidirect |
| 182. C79 | C2×#1629 | semidirect |
| 264. C2×D4 | #11929612 | semidirect |
| 311. D4 | C2×#11929612 | semidirect |
| 348. C2 | #23762516 | 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×#19098853 | 2 |
| #23762516 | 2 |
| C2×#19098307 | 2 |
| C2×D4⋊(C79⋊C8) | 2 |
| C2×D42×C79 | 2 |
| C2×#1629 | 79 |