Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 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×D8×D167 | C2 | semidirect |
| 2. #24923904 | C2 | semidirect |
| 3. #24923502 | C2 | semidirect |
| 4. #24923461 | C2 | semidirect |
| 5. #24923401 | C2 | semidirect |
| 6. C4×D1336 | C2 | semidirect |
| 7. C8×D668 | C2 | semidirect |
| 8. #493×C167 | C2 | semidirect |
| 10. C2×D4×D167 | C22 | semidirect |
| 12. C2×#14581935 | C22 | semidirect |
| 14. C2×C8×D167 | C22 | semidirect |
| 16. #19128803 | C22 | semidirect |
| 19. C4×D668 | C22 | semidirect |
| 20. #19128766 | C22 | semidirect |
| 21. C4⋊(C167⋊C8) | C22 | semidirect |
| 22. #19128754 | C22 | semidirect |
| 23. #19128753 | C22 | semidirect |
| 24. (C2×D167)⋊C8 | C22 | semidirect |
| 25. C2×D8×C167 | C22 | semidirect |
| 26. C2×D8×C167 | C22 | semidirect |
| 27. #127×C167 | C22 | semidirect |
| 28. C4×C8×C167 | C22 | semidirect |
| 39. D1336 | D4 | semidirect |
| 62. D668 | D8 | semidirect |
| 63. D668 | C2×D4 | semidirect |
| 81. C8×C167 | C2×D4 | semidirect |
| 92. C2×D167 | C2×D8 | semidirect |
| 94. C4×C167 | C2×D8 | semidirect |
| 105. C167 | D4×D8 | semidirect |
| 109. #493 | D167 | semidirect |
| 120. C2×D8 | C2×D167 | semidirect |
| 121. C2×D8 | C2×D167 | semidirect |
| 123. #127 | C2×D167 | semidirect |
| 134. C4×C8 | C2×D167 | semidirect |
| 187. C8 | D4×D167 | semidirect |
| 202. C4 | D8×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D167 | 2 |
| #24923904 | 2 |
| #24923502 | 2 |
| #24923461 | 2 |
| #24923401 | 2 |
| C4×D1336 | 2 |
| C8×D668 | 2 |
| #493×C167 | 2 |
| D4×D8 | 167 |