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. #24923620 | C2 | semidirect |
| 4. #24923606 | C2 | semidirect |
| 5. #24923564 | C2 | semidirect |
| 6. #24923509 | C2 | semidirect |
| 7. #24923479 | C2 | semidirect |
| 8. #24923423 | C2 | semidirect |
| 10. #103×D167 | C2 | semidirect |
| 11. C4×Q16×C167 | C2 | semidirect |
| 81. D668 | Q16 | semidirect |
| 122. C167 | #3299 | semidirect |
| 132. C4×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923979 | 2 |
| Q8×D668 | 2 |
| #24923620 | 2 |
| #24923606 | 2 |
| #24923564 | 2 |
| #24923509 | 2 |
| #24923479 | 2 |
| #24923423 | 2 |
| C8×D668 | 2 |
| #103×D167 | 2 |
| C4×Q16×C167 | 2 |
| #3299 | 167 |