Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24923648 | C2 | semidirect |
| 5. #24923479 | C2 | semidirect |
| 6. #24923476 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923374 | C2 | semidirect |
| 11. #557×C167 | C2 | semidirect |
| 119. C167 | #3398 | semidirect |
| 121. #557 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| #24923661 | 2 |
| #24923648 | 2 |
| #24923491 | 2 |
| #24923479 | 2 |
| #24923476 | 2 |
| #24923471 | 2 |
| #24923400 | 2 |
| #24923374 | 2 |
| C4×#14581937 | 2 |
| #557×C167 | 2 |
| #3398 | 167 |