Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
488 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 488 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. #24923814 | C2 | semidirect |
| 2. C2×#19128794 | C2 | semidirect |
| 3. #24923587 | C2 | semidirect |
| 4. #24923558 | C2 | semidirect |
| 5. #24923463 | C2 | semidirect |
| 6. #24923405 | C2 | semidirect |
| 7. #24923402 | C2 | semidirect |
| 8. #24923380 | C2 | semidirect |
| 9. #24923378 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #481×C167 | C2 | semidirect |
| 17. #19128831 | C22 | semidirect |
| 18. #19128828 | C22 | semidirect |
| 22. D4×Dic167 | C22 | semidirect |
| 27. #19128794 | C22 | semidirect |
| 31. #19128763 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 35. #19128752 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 40. #106×C167 | C22 | semidirect |
| 41. #102×C167 | C22 | semidirect |
| 92. D668 | #41 | semidirect |
| 149. C167 | #3109 | semidirect |
| 154. #481 | D167 | semidirect |
| 184. #106 | C2×D167 | semidirect |
| 189. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923814 | 2 |
| C2×#19128794 | 2 |
| #24923587 | 2 |
| #24923558 | 2 |
| #24923463 | 2 |
| #24923405 | 2 |
| #24923402 | 2 |
| #24923380 | 2 |
| #24923378 | 2 |
| #24923323 | 2 |
| #481×C167 | 2 |
| #3109 | 167 |