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. #24923620 | C2 | semidirect |
| 4. #24923601 | C2 | semidirect |
| 5. #24923554 | C2 | semidirect |
| 6. #24923497 | C2 | semidirect |
| 7. #24923474 | C2 | semidirect |
| 8. #24923406 | C2 | semidirect |
| 9. C8×D668 | C2 | semidirect |
| 10. #103×D167 | C2 | semidirect |
| 11. C4×SD16×C167 | C2 | semidirect |
| 82. D668 | SD16 | semidirect |
| 94. Q8×C167 | #41 | semidirect |
| 128. C167 | #3298 | semidirect |
| 138. C4×SD16 | D167 | semidirect |
| 213. Q8 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D668 | 2 |
| #24923924 | 2 |
| #24923620 | 2 |
| #24923601 | 2 |
| #24923554 | 2 |
| #24923497 | 2 |
| #24923474 | 2 |
| #24923406 | 2 |
| C8×D668 | 2 |
| #103×D167 | 2 |
| C4×SD16×C167 | 2 |
| #3298 | 167 |