Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #24923819 | C2 | semidirect |
| 2. #24923679 | C2 | semidirect |
| 3. #24923659 | C2 | semidirect |
| 4. #24923635 | C2 | semidirect |
| 5. #24923628 | C2 | semidirect |
| 6. #24923520 | C2 | semidirect |
| 7. #24923517 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. C4×#14581935 | C2 | semidirect |
| 10. C4×#14581934 | C2 | semidirect |
| 11. #529×C167 | C2 | semidirect |
| 92. C167⋊C8 | #41 | semidirect |
| 137. C167 | #3171 | semidirect |
| 140. #529 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| #24923679 | 2 |
| #24923659 | 2 |
| #24923635 | 2 |
| #24923628 | 2 |
| #24923520 | 2 |
| #24923517 | 2 |
| C4×#14581937 | 2 |
| C4×#14581935 | 2 |
| C4×#14581934 | 2 |
| #529×C167 | 2 |
| #3171 | 167 |