Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923998 | C2 | semidirect |
| 3. #24923625 | C2 | semidirect |
| 5. #24923572 | C2 | semidirect |
| 6. #24923554 | C2 | semidirect |
| 7. #24923493 | C2 | semidirect |
| 9. C8×Dic334 | C2 | semidirect |
| 10. #24923354 | C2 | semidirect |
| 11. C4×Q16×C167 | C2 | semidirect |
| 117. C167 | #3365 | semidirect |
| 128. C4×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923998 | 2 |
| #24923625 | 2 |
| #24923616 | 2 |
| #24923572 | 2 |
| #24923554 | 2 |
| #24923493 | 2 |
| #24923469 | 2 |
| C8×Dic334 | 2 |
| #24923354 | 2 |
| C4×Q16×C167 | 2 |
| #3365 | 167 |