Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic334 | C2 | semidirect |
| 2. C2×#19128862 | C2 | semidirect |
| 3. #24923424 | C2 | semidirect |
| 4. #24923407 | C2 | semidirect |
| 5. #24923277 | C2 | semidirect |
| 6. #24923233 | C2 | semidirect |
| 15. C2×#14581940 | C22 | semidirect |
| 16. C2×#14581938 | C22 | semidirect |
| 18. #19128755 | C22 | semidirect |
| 34. C2×Dic334 | D4 | semidirect |
| 95. C22×C167 | #137 | semidirect |
| 108. C167 | #3004 | semidirect |
| 204. C22 | #19128862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic334 | 2 |
| C2×#19128862 | 2 |
| #24923424 | 2 |
| #24923407 | 2 |
| #24923277 | 2 |
| #24923233 | 2 |
| #525×C167 | 2 |
| #3004 | 167 |