Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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×Dic334 | C2 | semidirect |
| 3. #24923616 | C2 | semidirect |
| 4. #24923614 | C2 | semidirect |
| 5. #24923559 | C2 | semidirect |
| 6. #24923558 | C2 | semidirect |
| 7. #24923469 | C2 | semidirect |
| 8. #24923467 | C2 | semidirect |
| 9. C8×Dic334 | C2 | semidirect |
| 10. #24923354 | C2 | semidirect |
| 11. C4×SD16×C167 | C2 | semidirect |
| 77. Dic334 | SD16 | semidirect |
| 91. Q8×C167 | #41 | semidirect |
| 125. C167 | #3362 | semidirect |
| 137. C4×SD16 | D167 | semidirect |
| 206. Q8 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic334 | 2 |
| #24923940 | 2 |
| #24923616 | 2 |
| #24923614 | 2 |
| #24923559 | 2 |
| #24923558 | 2 |
| #24923469 | 2 |
| #24923467 | 2 |
| C8×Dic334 | 2 |
| #24923354 | 2 |
| C4×SD16×C167 | 2 |
| #3362 | 167 |