Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. #24923819 | C2 | semidirect |
| 2. C4×#14581950 | C2 | semidirect |
| 3. #24923594 | C2 | semidirect |
| 4. #24923555 | C2 | semidirect |
| 5. #24923550 | C2 | semidirect |
| 6. #24923470 | C2 | semidirect |
| 7. #24923465 | C2 | semidirect |
| 8. #24923416 | C2 | semidirect |
| 9. #24923382 | C2 | semidirect |
| 10. #24923371 | C2 | semidirect |
| 11. #432×C167 | C2 | semidirect |
| 87. Dic334 | #41 | semidirect |
| 93. D668 | #41 | semidirect |
| 144. C167 | #3115 | semidirect |
| 156. #432 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| C4×#14581950 | 2 |
| #24923594 | 2 |
| #24923555 | 2 |
| #24923550 | 2 |
| #24923470 | 2 |
| #24923465 | 2 |
| #24923416 | 2 |
| #24923382 | 2 |
| #24923371 | 2 |
| #432×C167 | 2 |
| #3115 | 167 |