Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923997 | C2 | semidirect |
| 4. #24923649 | C2 | semidirect |
| 6. #24923479 | C2 | semidirect |
| 7. #24923478 | C2 | semidirect |
| 9. #24923399 | C2 | semidirect |
| 10. #24923375 | C2 | semidirect |
| 119. C167 | #3398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923997 | 2 |
| #24923989 | 2 |
| #24923660 | 2 |
| #24923649 | 2 |
| #24923490 | 2 |
| #24923479 | 2 |
| #24923478 | 2 |
| #24923474 | 2 |
| #24923399 | 2 |
| #24923375 | 2 |
| C4×SD16×C167 | 2 |
| #3398 | 167 |