Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D668 | C2 | semidirect |
| 3. #24923621 | C2 | semidirect |
| 4. #24923601 | C2 | semidirect |
| 5. #24923499 | C2 | semidirect |
| 6. #24923475 | C2 | semidirect |
| 7. #24923409 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. #24923334 | C2 | semidirect |
| 10. #103×D167 | C2 | semidirect |
| 11. #475×C167 | C2 | semidirect |
| 85. D668 | SD16 | semidirect |
| 98. Q8×C167 | #41 | semidirect |
| 128. C167 | #3298 | semidirect |
| 134. #475 | D167 | semidirect |
| 213. Q8 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D668 | 2 |
| #24923922 | 2 |
| #24923621 | 2 |
| #24923601 | 2 |
| #24923499 | 2 |
| #24923475 | 2 |
| #24923409 | 2 |
| C4×#14581937 | 2 |
| #24923334 | 2 |
| #103×D167 | 2 |
| #475×C167 | 2 |
| #3298 | 167 |