Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×#19104697 | C2 | semidirect |
| 3. #23781776 | C2 | direct (N × H) |
| 4. C2×#19104655 | C2 | semidirect |
| 5. C2×#19104645 | C2 | semidirect |
| 6. C2×#106×C163 | C2 | semidirect |
| 9. C2×D1304 | C4 | semidirect |
| 13. #19104697 | C22 | semidirect |
| 16. #19104655 | C22 | semidirect |
| 17. #19104645 | C22 | semidirect |
| 20. #106×C163 | C22 | semidirect |
| 24. C2×D652 | C2×C4 | semidirect |
| 29. D1304 | C2×C4 | semidirect |
| 37. C2×C8×C163 | C2×C4 | semidirect |
| 47. D652 | C22×C4 | semidirect |
| 59. C8×C163 | C22×C4 | semidirect |
| 72. C2×C163 | #442 | semidirect |
| 76. C163 | C2×#442 | semidirect |
| 81. C2×#106 | D163 | semidirect |
| 95. #106 | C2×D163 | semidirect |
| 111. C2×C8 | C4×D163 | semidirect |
| 136. C8 | C2×C4×D163 | semidirect |
| 150. C2 | #23781776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1304 | 2 |
| C2×#19104697 | 2 |
| #23781776 | 2 |
| C2×#19104655 | 2 |
| C2×#19104645 | 2 |
| C2×#106×C163 | 2 |
| C2×#442 | 163 |