Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
546 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19128859 | C2 | semidirect |
| 2. #24923922 | C2 | semidirect |
| 3. #24923904 | C2 | semidirect |
| 4. #24923512 | C2 | semidirect |
| 5. #24923471 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923418 | C2 | semidirect |
| 8. #24923413 | C2 | semidirect |
| 9. C4×D1336 | C2 | semidirect |
| 10. #24923348 | C2 | semidirect |
| 11. #492×C167 | C2 | semidirect |
| 12. C2×#14581951 | C22 | semidirect |
| 18. C2×#14581935 | C22 | semidirect |
| 19. C2×#14581933 | C22 | semidirect |
| 21. #19128808 | C22 | semidirect |
| 28. C4×D668 | C22 | semidirect |
| 30. #19128766 | C22 | semidirect |
| 31. C4⋊(C167⋊C8) | C22 | semidirect |
| 32. #19128756 | C22 | semidirect |
| 34. #19128754 | C22 | semidirect |
| 35. #19128753 | C22 | semidirect |
| 36. (C2×D167)⋊C8 | C22 | semidirect |
| 37. C2×SD16×C167 | C22 | semidirect |
| 38. C2×SD16×C167 | C22 | semidirect |
| 39. C4⋊Q8×C167 | C22 | semidirect |
| 41. C4×C8×C167 | C22 | semidirect |
| 59. D1336 | D4 | semidirect |
| 94. D668 | C2×D4 | semidirect |
| 118. C8×C167 | C2×D4 | semidirect |
| 135. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 148. C167 | #3272 | semidirect |
| 153. #492 | D167 | semidirect |
| 166. C2×SD16 | C2×D167 | semidirect |
| 167. C2×SD16 | C2×D167 | semidirect |
| 171. C4⋊Q8 | C2×D167 | semidirect |
| 190. C4×C8 | C2×D167 | semidirect |
| 267. C8 | D4×D167 | semidirect |
| 287. C4 | #19128859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128859 | 2 |
| #24923922 | 2 |
| #24923904 | 2 |
| #24923512 | 2 |
| #24923471 | 2 |
| #24923461 | 2 |
| #24923418 | 2 |
| #24923413 | 2 |
| C4×D1336 | 2 |
| #24923348 | 2 |
| #492×C167 | 2 |
| #3272 | 167 |