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. #24924001 | C2 | semidirect |
| 2. #24923654 | C2 | semidirect |
| 4. #24923486 | C2 | semidirect |
| 5. #24923481 | C2 | semidirect |
| 6. #24923467 | C2 | semidirect |
| 7. C8×Dic334 | C2 | semidirect |
| 8. Q16×Dic167 | C2 | semidirect |
| 9. C4×D1336 | C2 | semidirect |
| 10. D8×Dic167 | C2 | semidirect |
| 11. #495×C167 | C2 | semidirect |
| 120. C167 | #3396 | semidirect |
| 124. #495 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924001 | 2 |
| #24923654 | 2 |
| #24923644 | 2 |
| #24923486 | 2 |
| #24923481 | 2 |
| #24923467 | 2 |
| C8×Dic334 | 2 |
| Q16×Dic167 | 2 |
| C4×D1336 | 2 |
| D8×Dic167 | 2 |
| #495×C167 | 2 |
| #3396 | 167 |