Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #24923621 | C2 | semidirect |
| 4. #24923606 | C2 | semidirect |
| 5. #24923511 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923426 | C2 | semidirect |
| 8. C4×#14581940 | C2 | semidirect |
| 10. #103×D167 | C2 | semidirect |
| 11. #477×C167 | C2 | semidirect |
| 82. D668 | Q16 | semidirect |
| 122. C167 | #3299 | semidirect |
| 128. #477 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923980 | 2 |
| Q8×D668 | 2 |
| #24923621 | 2 |
| #24923606 | 2 |
| #24923511 | 2 |
| #24923480 | 2 |
| #24923426 | 2 |
| C4×#14581940 | 2 |
| #24923334 | 2 |
| #103×D167 | 2 |
| #477×C167 | 2 |
| #3299 | 167 |