Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 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. #24924002 | C2 | semidirect |
| 2. #24923653 | C2 | semidirect |
| 3. #24923652 | C2 | semidirect |
| 5. #24923484 | C2 | semidirect |
| 6. #24923483 | C2 | semidirect |
| 7. #24923468 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 9. #24923363 | C2 | semidirect |
| 10. #24923351 | C2 | semidirect |
| 11. C4×D8×C167 | C2 | semidirect |
| 120. C167 | #3396 | semidirect |
| 132. C4×D8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924002 | 2 |
| #24923653 | 2 |
| #24923652 | 2 |
| #24923644 | 2 |
| #24923484 | 2 |
| #24923483 | 2 |
| #24923468 | 2 |
| C8×Dic334 | 2 |
| #24923363 | 2 |
| #24923351 | 2 |
| C4×D8×C167 | 2 |
| #3396 | 167 |