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. C4×#14581950 | C2 | semidirect |
| 2. #24923590 | C2 | semidirect |
| 3. #24923551 | C2 | semidirect |
| 4. #24923546 | C2 | semidirect |
| 5. #24923466 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923412 | C2 | semidirect |
| 8. #24923379 | C2 | semidirect |
| 9. #24923369 | C2 | semidirect |
| 10. #24923326 | C2 | semidirect |
| 11. #532×C167 | C2 | semidirect |
| 85. Dic334 | #41 | semidirect |
| 87. D668 | #41 | semidirect |
| 144. C167 | #3115 | semidirect |
| 146. #532 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581950 | 2 |
| #24923590 | 2 |
| #24923551 | 2 |
| #24923546 | 2 |
| #24923466 | 2 |
| #24923461 | 2 |
| #24923412 | 2 |
| #24923379 | 2 |
| #24923369 | 2 |
| #24923326 | 2 |
| #532×C167 | 2 |
| #3115 | 167 |