Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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. #125×D167 | C2 | semidirect |
| 3. #24923626 | C2 | semidirect |
| 4. #24923625 | C2 | semidirect |
| 5. #24923624 | C2 | semidirect |
| 6. #24923623 | C2 | semidirect |
| 7. #24923622 | C2 | semidirect |
| 8. #103×D167 | C2 | semidirect |
| 10. C4×C8×D167 | C2 | semidirect |
| 11. #488×C167 | C2 | semidirect |
| 15. #19128824 | C22 | semidirect |
| 16. #19128823 | C22 | semidirect |
| 26. #19128757 | C22 | semidirect |
| 27. #19128756 | C22 | semidirect |
| 28. #19128755 | C22 | semidirect |
| 32. C4×C167⋊C8 | C22 | semidirect |
| 33. C8×Dic167 | C22 | semidirect |
| 34. #125×C167 | C22 | semidirect |
| 36. #103×C167 | C22 | semidirect |
| 38. C4×C8×C167 | C22 | semidirect |
| 114. D167 | #488 | direct (N × H) |
| 115. C167 | C2×#488 | semidirect |
| 124. #488 | D167 | direct (N × H) |
| 134. #125 | C2×D167 | semidirect |
| 147. #103 | C2×D167 | semidirect |
| 154. C4×C8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D167 | 2 |
| #124×D167 | 2 |
| #24923626 | 2 |
| #24923625 | 2 |
| #24923624 | 2 |
| #24923623 | 2 |
| #24923622 | 2 |
| #103×D167 | 2 |
| #102×D167 | 2 |
| C4×C8×D167 | 2 |
| #488×C167 | 2 |
| C2×#488 | 167 |