Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923820 | C2 | semidirect |
| 2. C4×D4×D167 | C2 | semidirect |
| 3. #24923589 | C2 | semidirect |
| 4. #24923556 | C2 | semidirect |
| 5. #24923465 | C2 | semidirect |
| 6. #24923464 | C2 | semidirect |
| 7. #24923404 | C2 | semidirect |
| 8. #24923380 | C2 | semidirect |
| 9. #24923378 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #476×C167 | C2 | semidirect |
| 17. #19128829 | C22 | semidirect |
| 25. #19128794 | C22 | semidirect |
| 31. #19128763 | C22 | semidirect |
| 32. C4⋊(C167⋊C8) | C22 | semidirect |
| 33. #19128754 | C22 | semidirect |
| 35. #19128752 | C22 | semidirect |
| 37. #19128742 | C22 | semidirect |
| 38. C4⋊Q8×C167 | C22 | semidirect |
| 40. #106×C167 | C22 | semidirect |
| 41. C4⋊C8×C167 | C22 | semidirect |
| 96. D668 | #41 | semidirect |
| 115. D4×C167 | #41 | semidirect |
| 154. C167 | #3109 | semidirect |
| 160. #476 | D167 | semidirect |
| 172. C4⋊Q8 | C2×D167 | semidirect |
| 189. #106 | C2×D167 | semidirect |
| 191. C4⋊C8 | C2×D167 | semidirect |
| 256. D4 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923820 | 2 |
| C4×D4×D167 | 2 |
| #24923589 | 2 |
| #24923556 | 2 |
| #24923465 | 2 |
| #24923464 | 2 |
| #24923404 | 2 |
| #24923380 | 2 |
| #24923378 | 2 |
| #24923325 | 2 |
| #476×C167 | 2 |
| #3109 | 167 |