Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #24923286 | C2 | semidirect |
| 3. C2×#19128760 | C2 | semidirect |
| 4. #24923242 | C2 | semidirect |
| 5. #24923039 | C2 | semidirect |
| 6. #24923029 | C2 | semidirect |
| 7. C4×#41×C167 | C2 | semidirect |
| 10. #19128862 | C4 | semidirect |
| 12. #19128857 | C4 | semidirect |
| 33. C2×Dic334 | C2×C4 | semidirect |
| 34. C2×D668 | C2×C4 | semidirect |
| 44. #14581934 | C2×C4 | semidirect |
| 129. C167 | #1906 | semidirect |
| 132. C4×#41 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924067 | 2 |
| #24923286 | 2 |
| C2×#19128760 | 2 |
| #24923242 | 2 |
| #24923039 | 2 |
| #24923029 | 2 |
| C4×#41×C167 | 2 |
| #1906 | 167 |