Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24923821 | C2 | semidirect |
| 3. #24923605 | C2 | semidirect |
| 4. #24923602 | C2 | semidirect |
| 5. #24923547 | C2 | semidirect |
| 6. #24923472 | C2 | semidirect |
| 8. #24923370 | C2 | semidirect |
| 9. #24923366 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 14. #19128831 | C22 | semidirect |
| 15. #19128830 | C22 | semidirect |
| 19. Q8×Dic167 | C22 | semidirect |
| 21. #19128797 | C22 | semidirect |
| 30. #19128766 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 33. #19128757 | C22 | semidirect |
| 34. #19128756 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 136. C167 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923821 | 2 |
| C2×D4×Dic167 | 2 |
| #24923605 | 2 |
| #24923602 | 2 |
| #24923547 | 2 |
| #24923472 | 2 |
| #24923420 | 2 |
| #24923370 | 2 |
| #24923366 | 2 |
| #24923323 | 2 |
| #450×C167 | 2 |
| #3110 | 167 |