Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 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. #24923800 | C2 | semidirect |
| 2. C2×#19128794 | C2 | semidirect |
| 3. #24923599 | C2 | semidirect |
| 4. #24923572 | C2 | semidirect |
| 5. #24923483 | C2 | semidirect |
| 6. #24923422 | C2 | semidirect |
| 8. #24923378 | C2 | semidirect |
| 9. #24923368 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #480×C167 | C2 | semidirect |
| 17. #19128823 | C22 | semidirect |
| 18. #19128819 | C22 | semidirect |
| 21. #19128797 | C22 | semidirect |
| 23. D4×Dic167 | C22 | semidirect |
| 31. #19128763 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 33. #19128755 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 40. #107×C167 | C22 | semidirect |
| 41. #102×C167 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
| 145. #480 | D167 | semidirect |
| 174. #107 | C2×D167 | semidirect |
| 180. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923800 | 2 |
| C2×#19128794 | 2 |
| #24923599 | 2 |
| #24923572 | 2 |
| #24923483 | 2 |
| #24923422 | 2 |
| #24923402 | 2 |
| #24923378 | 2 |
| #24923368 | 2 |
| #24923323 | 2 |
| #480×C167 | 2 |
| #3114 | 167 |