Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782466 | C2 | semidirect |
| 2. #23781932 | C2 | semidirect |
| 3. #23781832 | C2 | semidirect |
| 4. #23781783 | C2 | semidirect |
| 5. #493×C163 | C2 | semidirect |
| 6. #19104780 | C22 | semidirect |
| 7. #19104761 | C22 | semidirect |
| 12. #19104741 | C22 | semidirect |
| 13. #19104671 | C22 | semidirect |
| 14. #19104663 | C22 | semidirect |
| 15. #19104652 | C22 | semidirect |
| 16. C2×D8×C163 | C22 | semidirect |
| 17. #127×C163 | C22 | semidirect |
| 18. C4×C8×C163 | C22 | semidirect |
| 23. Dic652 | D4 | semidirect |
| 24. #14579688 | D4 | semidirect |
| 26. D1304 | D4 | semidirect |
| 64. C163 | #3292 | semidirect |
| 67. #493 | D163 | semidirect |
| 77. C2×D8 | C2×D163 | semidirect |
| 79. #127 | C2×D163 | semidirect |
| 83. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782466 | 2 |
| #23781932 | 2 |
| #23781832 | 2 |
| #23781783 | 2 |
| #493×C163 | 2 |
| #3292 | 163 |