Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19128851 | C2 | semidirect |
| 2. C2×Q16×D167 | C2 | semidirect |
| 3. #24923927 | C2 | semidirect |
| 4. #24923507 | C2 | semidirect |
| 5. #24923502 | C2 | semidirect |
| 6. #24923488 | C2 | semidirect |
| 7. #24923428 | C2 | semidirect |
| 8. #24923406 | C2 | semidirect |
| 9. C4×Dic668 | C2 | semidirect |
| 10. C8×D668 | C2 | semidirect |
| 11. #495×C167 | C2 | semidirect |
| 54. Dic668 | D4 | semidirect |
| 120. C2×D167 | #135 | semidirect |
| 136. C167 | #3285 | semidirect |
| 141. #495 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128851 | 2 |
| C2×Q16×D167 | 2 |
| #24923927 | 2 |
| #24923507 | 2 |
| #24923502 | 2 |
| #24923488 | 2 |
| #24923428 | 2 |
| #24923406 | 2 |
| C4×Dic668 | 2 |
| C8×D668 | 2 |
| #495×C167 | 2 |
| #3285 | 167 |