Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 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. C2×#19128854 | C2 | semidirect |
| 2. C2×#19128851 | C2 | semidirect |
| 3. #24923937 | C2 | semidirect |
| 4. #24923644 | C2 | semidirect |
| 5. #24923506 | C2 | semidirect |
| 6. #24923468 | C2 | semidirect |
| 7. #24923415 | C2 | semidirect |
| 8. #24923412 | C2 | semidirect |
| 9. #24923363 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. #466×C167 | C2 | semidirect |
| 56. Dic668 | D4 | semidirect |
| 134. Dic167 | #135 | semidirect |
| 142. C167 | #3287 | semidirect |
| 149. #466 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| C2×#19128851 | 2 |
| #24923937 | 2 |
| #24923644 | 2 |
| #24923506 | 2 |
| #24923468 | 2 |
| #24923415 | 2 |
| #24923412 | 2 |
| #24923363 | 2 |
| C8×C22⋊D167 | 2 |
| #466×C167 | 2 |
| #3287 | 167 |