Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #24923922 | C2 | semidirect |
| 2. #24923904 | C2 | semidirect |
| 3. #24923581 | C2 | semidirect |
| 4. #24923546 | C2 | semidirect |
| 5. #24923504 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923404 | C2 | semidirect |
| 8. C4×D1336 | C2 | semidirect |
| 9. C8×D668 | C2 | semidirect |
| 10. #102×D167 | C2 | semidirect |
| 11. #486×C167 | C2 | semidirect |
| 16. C2×#14581935 | C22 | semidirect |
| 17. C2×C8×D167 | C22 | semidirect |
| 20. #19128807 | C22 | semidirect |
| 26. C4×D668 | C22 | semidirect |
| 27. C4⋊C4×D167 | C22 | semidirect |
| 28. #19128766 | C22 | semidirect |
| 29. #19128765 | C22 | semidirect |
| 30. C4⋊(C167⋊C8) | C22 | semidirect |
| 32. #19128754 | C22 | semidirect |
| 33. #19128753 | C22 | semidirect |
| 35. (C2×D167)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C167 | C22 | semidirect |
| 38. #102×C167 | C22 | semidirect |
| 39. #102×C167 | C22 | semidirect |
| 40. C4×C8×C167 | C22 | semidirect |
| 88. D668 | D8 | semidirect |
| 89. D668 | #41 | semidirect |
| 142. C167 | #3294 | semidirect |
| 146. #486 | D167 | semidirect |
| 161. C4⋊Q8 | C2×D167 | semidirect |
| 180. #102 | C2×D167 | semidirect |
| 181. #102 | C2×D167 | semidirect |
| 183. C4×C8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923922 | 2 |
| #24923904 | 2 |
| #24923581 | 2 |
| #24923546 | 2 |
| #24923504 | 2 |
| #24923461 | 2 |
| #24923404 | 2 |
| C4×D1336 | 2 |
| C8×D668 | 2 |
| #102×D167 | 2 |
| #486×C167 | 2 |
| #3294 | 167 |