Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24923820 | C2 | semidirect |
| 2. C4×#14581951 | C2 | semidirect |
| 3. #24923595 | C2 | semidirect |
| 4. #24923546 | C2 | semidirect |
| 5. #24923469 | C2 | semidirect |
| 6. #24923465 | C2 | semidirect |
| 7. #24923417 | C2 | semidirect |
| 8. #24923380 | C2 | semidirect |
| 9. #24923372 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #475×C167 | C2 | semidirect |
| 93. D668 | #41 | semidirect |
| 109. Q8×C167 | #41 | semidirect |
| 144. C167 | #3115 | semidirect |
| 149. #475 | D167 | semidirect |
| 233. Q8 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923820 | 2 |
| C4×#14581951 | 2 |
| #24923595 | 2 |
| #24923546 | 2 |
| #24923469 | 2 |
| #24923465 | 2 |
| #24923417 | 2 |
| #24923380 | 2 |
| #24923372 | 2 |
| #24923325 | 2 |
| #475×C167 | 2 |
| #3115 | 167 |