Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24923604 | C2 | semidirect |
| 4. #24923548 | C2 | semidirect |
| 5. #24923473 | C2 | semidirect |
| 8. #24923372 | C2 | semidirect |
| 9. #24923368 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #484×C167 | C2 | semidirect |
| 16. #19128831 | C22 | semidirect |
| 17. #19128830 | C22 | semidirect |
| 21. Q8×Dic167 | C22 | semidirect |
| 23. #19128797 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 33. #19128755 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 40. #107×C167 | C22 | semidirect |
| 41. #103×C167 | C22 | semidirect |
| 136. C167 | #3110 | semidirect |
| 141. #484 | D167 | semidirect |
| 171. #107 | C2×D167 | semidirect |
| 174. #103 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923821 | 2 |
| C2×#19128794 | 2 |
| #24923604 | 2 |
| #24923548 | 2 |
| #24923473 | 2 |
| #24923422 | 2 |
| #24923419 | 2 |
| #24923372 | 2 |
| #24923368 | 2 |
| #24923323 | 2 |
| #484×C167 | 2 |
| #3110 | 167 |