Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128858 | C2 | semidirect |
| 2. #24923940 | C2 | semidirect |
| 3. #24923645 | C2 | semidirect |
| 4. #24923520 | C2 | semidirect |
| 5. #24923466 | C2 | semidirect |
| 6. #24923464 | C2 | semidirect |
| 7. #24923412 | C2 | semidirect |
| 8. #24923403 | C2 | semidirect |
| 9. C4×#14581938 | C2 | semidirect |
| 10. #24923347 | C2 | semidirect |
| 11. D42×C167 | C2 | semidirect |
| 12. C2×#14581950 | C22 | semidirect |
| 15. C2×#14581938 | C22 | semidirect |
| 17. C2×#14581935 | C22 | semidirect |
| 18. C2×#14581935 | C22 | semidirect |
| 19. C2×#14581934 | C22 | semidirect |
| 20. #19128829 | C22 | semidirect |
| 22. #19128806 | C22 | semidirect |
| 24. C4×Dic334 | C22 | semidirect |
| 26. #19128763 | C22 | semidirect |
| 27. C4⋊(C167⋊C8) | C22 | semidirect |
| 28. #19128755 | C22 | semidirect |
| 30. #19128753 | C22 | semidirect |
| 31. #19128752 | C22 | semidirect |
| 32. C22⋊(C167⋊C8) | C22 | semidirect |
| 33. C4×C167⋊C8 | C22 | semidirect |
| 52. #14581938 | D4 | semidirect |
| 85. Dic334 | C2×D4 | semidirect |
| 97. C167⋊C8 | C2×D4 | semidirect |
| 138. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 150. C167 | #3274 | semidirect |
| 154. D42 | D167 | semidirect |
| 291. C4 | #19128858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128858 | 2 |
| #24923940 | 2 |
| #24923645 | 2 |
| #24923520 | 2 |
| #24923466 | 2 |
| #24923464 | 2 |
| #24923412 | 2 |
| #24923403 | 2 |
| C4×#14581938 | 2 |
| #24923347 | 2 |
| D42×C167 | 2 |
| #3274 | 167 |