Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #24923620 | C2 | semidirect |
| 4. #24923605 | C2 | semidirect |
| 5. #24923565 | C2 | semidirect |
| 6. #24923510 | C2 | semidirect |
| 7. #24923480 | C2 | semidirect |
| 8. #24923427 | C2 | semidirect |
| 9. C4×Dic668 | C2 | semidirect |
| 10. C2×#19128757 | C2 | semidirect |
| 93. D4×C167 | Q16 | semidirect |
| 122. C167 | #3299 | semidirect |
| 208. D4 | Dic668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923976 | 2 |
| D4×Dic334 | 2 |
| #24923620 | 2 |
| #24923605 | 2 |
| #24923565 | 2 |
| #24923510 | 2 |
| #24923480 | 2 |
| #24923427 | 2 |
| C4×Dic668 | 2 |
| C2×#19128757 | 2 |
| C8×D4×C167 | 2 |
| #3299 | 167 |