Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #24923976 | C2 | semidirect |
| 3. #24923616 | C2 | semidirect |
| 4. #24923588 | C2 | semidirect |
| 5. #24923560 | C2 | semidirect |
| 6. #24923498 | C2 | semidirect |
| 7. #24923470 | C2 | semidirect |
| 8. #24923422 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 10. C2×#19128754 | C2 | semidirect |
| 11. C8×D4×C167 | C2 | semidirect |
| 15. C2×#14581939 | C22 | semidirect |
| 16. #19128832 | C22 | semidirect |
| 19. #19128811 | C22 | semidirect |
| 24. C4×Dic334 | C22 | semidirect |
| 27. C2×C4⋊Dic167 | C22 | semidirect |
| 28. #19128764 | C22 | semidirect |
| 29. #19128764 | C22 | semidirect |
| 30. #19128757 | C22 | semidirect |
| 33. #19128754 | C22 | semidirect |
| 34. #19128754 | C22 | semidirect |
| 35. #19128754 | C22 | semidirect |
| 36. C22×C8×C167 | C22 | semidirect |
| 38. C4⋊C8×C167 | C22 | semidirect |
| 39. C22⋊C8×C167 | C22 | semidirect |
| 40. C4×C8×C167 | C22 | semidirect |
| 100. D4×C167 | SD16 | semidirect |
| 136. C167 | #3295 | semidirect |
| 147. C8×D4 | D167 | semidirect |
| 153. C22×C8 | C2×D167 | semidirect |
| 169. C4⋊C8 | C2×D167 | semidirect |
| 176. C22⋊C8 | C2×D167 | semidirect |
| 177. C4×C8 | C2×D167 | semidirect |
| 231. D4 | #14581939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923976 | 2 |
| D4×D668 | 2 |
| #24923616 | 2 |
| #24923588 | 2 |
| #24923560 | 2 |
| #24923498 | 2 |
| #24923470 | 2 |
| #24923422 | 2 |
| C4×#14581939 | 2 |
| C2×#19128754 | 2 |
| C8×D4×C167 | 2 |
| #3295 | 167 |