Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C2×Q8×Dic167 | C2 | semidirect |
| 3. #24923583 | C2 | semidirect |
| 4. #24923580 | C2 | semidirect |
| 5. #24923562 | C2 | semidirect |
| 6. #24923467 | C2 | semidirect |
| 7. #24923408 | C2 | semidirect |
| 8. #24923372 | C2 | semidirect |
| 9. #24923370 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #448×C167 | C2 | semidirect |
| 104. Q8×C167 | #41 | semidirect |
| 140. C167 | #3112 | semidirect |
| 149. #448 | D167 | semidirect |
| 229. Q8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923814 | 2 |
| C2×Q8×Dic167 | 2 |
| #24923583 | 2 |
| #24923580 | 2 |
| #24923562 | 2 |
| #24923467 | 2 |
| #24923408 | 2 |
| #24923372 | 2 |
| #24923370 | 2 |
| #24923323 | 2 |
| #448×C167 | 2 |
| #3112 | 167 |