Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24923803 | C2 | semidirect |
| 2. #24923599 | C2 | semidirect |
| 3. #24923582 | C2 | semidirect |
| 4. #24923569 | C2 | semidirect |
| 5. #24923484 | C2 | semidirect |
| 6. #24923420 | C2 | semidirect |
| 8. #24923379 | C2 | semidirect |
| 9. #24923369 | C2 | semidirect |
| 10. #24923326 | C2 | semidirect |
| 11. C2×C4×D4×C167 | C2 | semidirect |
| 15. #19128824 | C22 | semidirect |
| 16. #19128820 | C22 | semidirect |
| 20. C4×Dic334 | C22 | semidirect |
| 21. C4×D668 | C22 | semidirect |
| 24. #19128765 | C22 | semidirect |
| 25. #19128763 | C22 | semidirect |
| 26. C4⋊(C167⋊C8) | C22 | semidirect |
| 27. #19128755 | C22 | semidirect |
| 30. #19128752 | C22 | semidirect |
| 33. #19128743 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
| 143. C2×C4×D4 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923803 | 2 |
| #24923599 | 2 |
| #24923582 | 2 |
| #24923569 | 2 |
| #24923484 | 2 |
| #24923420 | 2 |
| #24923403 | 2 |
| #24923379 | 2 |
| #24923369 | 2 |
| #24923326 | 2 |
| C2×C4×D4×C167 | 2 |
| #3114 | 167 |