Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923912 | C2 | semidirect |
| 3. #24923512 | C2 | semidirect |
| 4. #24923481 | C2 | semidirect |
| 5. #24923430 | C2 | semidirect |
| 6. #24923401 | C2 | semidirect |
| 7. C4×D1336 | C2 | semidirect |
| 8. #24923348 | C2 | semidirect |
| 9. #495×C167 | C2 | semidirect |
| 11. C2×D4×D167 | C22 | semidirect |
| 13. C2×#14581937 | C22 | semidirect |
| 16. C2×#14581933 | C22 | semidirect |
| 18. #19128808 | C22 | semidirect |
| 23. C4×D668 | C22 | semidirect |
| 25. #19128766 | C22 | semidirect |
| 26. C4⋊(C167⋊C8) | C22 | semidirect |
| 27. #19128756 | C22 | semidirect |
| 28. #19128754 | C22 | semidirect |
| 29. #19128753 | C22 | semidirect |
| 30. (C2×D167)⋊C8 | C22 | semidirect |
| 31. C2×Q16×C167 | C22 | semidirect |
| 32. C2×SD16×C167 | C22 | semidirect |
| 34. #124×C167 | C22 | semidirect |
| 35. C4×C8×C167 | C22 | semidirect |
| 50. D1336 | D4 | semidirect |
| 124. C167 | #3273 | semidirect |
| 128. #495 | D167 | semidirect |
| 138. C2×Q16 | C2×D167 | semidirect |
| 140. C2×SD16 | C2×D167 | semidirect |
| 145. #124 | C2×D167 | semidirect |
| 160. C4×C8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128859 | 2 |
| #24923912 | 2 |
| #24923512 | 2 |
| #24923481 | 2 |
| #24923430 | 2 |
| #24923401 | 2 |
| C4×D1336 | 2 |
| #24923348 | 2 |
| #495×C167 | 2 |
| #3273 | 167 |