Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19128851 | C2 | semidirect |
| 2. C2×#19128838 | C2 | semidirect |
| 3. #24923848 | C2 | semidirect |
| 4. #24923514 | C2 | semidirect |
| 5. #24923513 | C2 | semidirect |
| 6. #24923511 | C2 | semidirect |
| 7. #24923510 | C2 | semidirect |
| 8. #24923502 | C2 | semidirect |
| 9. #107×D167 | C2 | semidirect |
| 10. #24923267 | C2 | semidirect |
| 11. #466×C167 | C2 | semidirect |
| 64. C8×D167 | D4 | semidirect |
| 143. C167 | #3061 | semidirect |
| 153. #466 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128851 | 2 |
| C2×#19128838 | 2 |
| #24923848 | 2 |
| #24923514 | 2 |
| #24923513 | 2 |
| #24923511 | 2 |
| #24923510 | 2 |
| #24923502 | 2 |
| #107×D167 | 2 |
| #24923267 | 2 |
| #466×C167 | 2 |
| #3061 | 167 |