Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #24923626 | C2 | semidirect |
| 4. #24923566 | C2 | semidirect |
| 5. #24923551 | C2 | semidirect |
| 6. #24923491 | C2 | semidirect |
| 8. Q8×C167⋊C8 | C2 | semidirect |
| 9. C4×#14581940 | C2 | semidirect |
| 10. C4×#14581937 | C2 | semidirect |
| 11. #557×C167 | C2 | semidirect |
| 117. C167 | #3365 | semidirect |
| 120. #557 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923626 | 2 |
| #24923617 | 2 |
| #24923566 | 2 |
| #24923551 | 2 |
| #24923491 | 2 |
| #24923469 | 2 |
| Q8×C167⋊C8 | 2 |
| C4×#14581940 | 2 |
| C4×#14581937 | 2 |
| #557×C167 | 2 |
| #3365 | 167 |