Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #24923923 | C2 | semidirect |
| 2. #24923615 | C2 | semidirect |
| 3. #24923580 | C2 | semidirect |
| 4. #24923549 | C2 | semidirect |
| 5. #24923503 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923403 | C2 | semidirect |
| 8. C4×#14581935 | C2 | semidirect |
| 9. D4×C167⋊C8 | C2 | semidirect |
| 10. C2×#19128753 | C2 | semidirect |
| 11. D42×C167 | C2 | semidirect |
| 14. C2×#14581935 | C22 | semidirect |
| 15. C22×C167⋊C8 | C22 | semidirect |
| 16. #19128832 | C22 | semidirect |
| 19. #19128806 | C22 | semidirect |
| 20. C4×D668 | C22 | semidirect |
| 21. C2×C4⋊Dic167 | C22 | semidirect |
| 22. #19128765 | C22 | semidirect |
| 23. #19128765 | C22 | semidirect |
| 24. C4⋊(C167⋊C8) | C22 | semidirect |
| 27. #19128753 | C22 | semidirect |
| 28. #19128753 | C22 | semidirect |
| 29. #19128753 | C22 | semidirect |
| 30. #19128752 | C22 | semidirect |
| 31. C22⋊(C167⋊C8) | C22 | semidirect |
| 32. C4×C167⋊C8 | C22 | semidirect |
| 103. D4×C167 | D8 | semidirect |
| 104. D4×C167 | #41 | semidirect |
| 142. C167 | #3294 | semidirect |
| 145. D42 | D167 | semidirect |
| 239. D4 | #14581935 | semidirect |
| 240. D4 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923923 | 2 |
| #24923615 | 2 |
| #24923580 | 2 |
| #24923549 | 2 |
| #24923503 | 2 |
| #24923461 | 2 |
| #24923403 | 2 |
| C4×#14581935 | 2 |
| D4×C167⋊C8 | 2 |
| C2×#19128753 | 2 |
| D42×C167 | 2 |
| #3294 | 167 |