Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. C2×C4×Dic334 | C2 | semidirect |
| 2. #24923602 | C2 | semidirect |
| 4. #24923573 | C2 | semidirect |
| 5. #24923488 | C2 | semidirect |
| 6. #24923424 | C2 | semidirect |
| 8. #24923374 | C2 | semidirect |
| 9. #24923369 | C2 | semidirect |
| 10. #24923326 | C2 | semidirect |
| 131. C167 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic334 | 2 |
| #24923602 | 2 |
| #24923585 | 2 |
| #24923573 | 2 |
| #24923488 | 2 |
| #24923424 | 2 |
| #24923407 | 2 |
| #24923374 | 2 |
| #24923369 | 2 |
| #24923326 | 2 |
| #529×C167 | 2 |
| #3117 | 167 |