Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #24923621 | C2 | semidirect |
| 4. #24923573 | C2 | semidirect |
| 7. #24923479 | C2 | semidirect |
| 8. Q8×C167⋊C8 | C2 | semidirect |
| 9. C4×#14581940 | C2 | semidirect |
| 11. #557×C167 | C2 | semidirect |
| 115. C167 | #3364 | semidirect |
| 117. #557 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| #24923626 | 2 |
| #24923621 | 2 |
| #24923573 | 2 |
| #24923546 | 2 |
| #24923491 | 2 |
| #24923479 | 2 |
| Q8×C167⋊C8 | 2 |
| C4×#14581940 | 2 |
| C4×#14581937 | 2 |
| #557×C167 | 2 |
| #3364 | 167 |