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. #24923805 | C2 | semidirect |
| 2. C2×#19128794 | C2 | semidirect |
| 3. #24923582 | C2 | semidirect |
| 4. #24923568 | C2 | semidirect |
| 5. #24923487 | C2 | semidirect |
| 6. #24923419 | C2 | semidirect |
| 8. #24923380 | C2 | semidirect |
| 9. #24923372 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #483×C167 | C2 | semidirect |
| 17. #19128823 | C22 | semidirect |
| 18. #19128821 | C22 | semidirect |
| 21. Q8×Dic167 | C22 | semidirect |
| 26. #19128794 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. Dic167⋊C8 | C22 | semidirect |
| 35. #19128752 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 40. #106×C167 | C22 | semidirect |
| 41. #103×C167 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
| 144. #483 | D167 | semidirect |
| 175. #106 | C2×D167 | semidirect |
| 177. #103 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923805 | 2 |
| C2×#19128794 | 2 |
| #24923582 | 2 |
| #24923568 | 2 |
| #24923487 | 2 |
| #24923419 | 2 |
| #24923405 | 2 |
| #24923380 | 2 |
| #24923372 | 2 |
| #24923323 | 2 |
| #483×C167 | 2 |
| #3114 | 167 |