Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24923886 | C2 | semidirect |
| 2. #24923673 | C2 | semidirect |
| 3. #24923652 | C2 | semidirect |
| 4. #24923627 | C2 | semidirect |
| 5. #24923513 | C2 | semidirect |
| 6. #24923510 | C2 | semidirect |
| 7. #24923366 | C2 | semidirect |
| 8. #24923363 | C2 | semidirect |
| 9. D8×Dic167 | C2 | semidirect |
| 10. #24923224 | C2 | semidirect |
| 117. C167 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923886 | 2 |
| #24923673 | 2 |
| #24923652 | 2 |
| #24923627 | 2 |
| #24923513 | 2 |
| #24923510 | 2 |
| #24923366 | 2 |
| #24923363 | 2 |
| D8×Dic167 | 2 |
| #24923224 | 2 |
| #466×C167 | 2 |
| #3175 | 167 |