Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24923979 | C2 | semidirect |
| 3. #24923615 | C2 | semidirect |
| 4. #24923586 | C2 | semidirect |
| 5. #24923560 | C2 | semidirect |
| 6. #24923495 | C2 | semidirect |
| 7. #24923418 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. #24923334 | C2 | semidirect |
| 10. #102×D167 | C2 | semidirect |
| 11. #460×C167 | C2 | semidirect |
| 15. C2×C8×D167 | C22 | semidirect |
| 16. #19128832 | C22 | semidirect |
| 19. #19128808 | C22 | semidirect |
| 26. C4⋊C4×D167 | C22 | semidirect |
| 27. #19128764 | C22 | semidirect |
| 28. #19128763 | C22 | semidirect |
| 29. #19128756 | C22 | semidirect |
| 31. #19128753 | C22 | semidirect |
| 32. #19128753 | C22 | semidirect |
| 34. (C2×D167)⋊C8 | C22 | semidirect |
| 35. C4×C167⋊C8 | C22 | semidirect |
| 36. C2×SD16×C167 | C22 | semidirect |
| 38. C4×Q8×C167 | C22 | semidirect |
| 39. C4⋊C8×C167 | C22 | semidirect |
| 40. #102×C167 | C22 | semidirect |
| 84. D668 | SD16 | semidirect |
| 136. C167 | #3295 | semidirect |
| 144. #460 | D167 | semidirect |
| 152. C2×SD16 | C2×D167 | semidirect |
| 162. C4×Q8 | C2×D167 | semidirect |
| 169. C4⋊C8 | C2×D167 | semidirect |
| 175. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923979 | 2 |
| #24923904 | 2 |
| #24923615 | 2 |
| #24923586 | 2 |
| #24923560 | 2 |
| #24923495 | 2 |
| #24923418 | 2 |
| C4×#14581937 | 2 |
| #24923334 | 2 |
| #102×D167 | 2 |
| #460×C167 | 2 |
| #3295 | 167 |