Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #24923149 | C2 | semidirect |
| 3. #24923148 | C2 | semidirect |
| 4. #24923147 | C2 | semidirect |
| 5. #24923146 | C2 | semidirect |
| 6. #24923145 | C2 | semidirect |
| 7. #24923145 | C2 | semidirect |
| 8. #24923136 | C2 | semidirect |
| 9. #386×C167 | C2 | semidirect |
| 15. #19128828 | C4 | semidirect |
| 35. C2×D668 | C2×C4 | semidirect |
| 40. C2×C22⋊D167 | C2×C4 | semidirect |
| 41. C2×C22⋊D167 | C2×C4 | semidirect |
| 55. C4×Dic167 | C2×C4 | semidirect |
| 60. C2×D4×C167 | C2×C4 | semidirect |
| 147. C167 | #2380 | semidirect |
| 156. #386 | D167 | semidirect |
| 194. C2×D4 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128828 | 2 |
| #24923149 | 2 |
| #24923148 | 2 |
| #24923147 | 2 |
| #24923146 | 2 |
| #24923145 | 2 |
| #24923136 | 2 |
| #386×C167 | 2 |
| #2380 | 167 |