Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C4⋊Dic167 | C2 | semidirect |
| 3. #24923605 | C2 | semidirect |
| 4. #24923600 | C2 | semidirect |
| 5. #24923588 | C2 | semidirect |
| 6. #24923583 | C2 | semidirect |
| 7. #24923311 | C2 | semidirect |
| 8. #24923271 | C2 | semidirect |
| 9. #407×C167 | C2 | semidirect |
| 27. #19128766 | C22 | semidirect |
| 28. #19128764 | C22 | semidirect |
| 29. #19128757 | C22 | semidirect |
| 30. #19128754 | C22 | semidirect |
| 130. C167 | #3092 | semidirect |
| 140. #407 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923780 | 2 |
| C22×C4⋊Dic167 | 2 |
| #24923605 | 2 |
| #24923600 | 2 |
| #24923588 | 2 |
| #24923583 | 2 |
| #24923311 | 2 |
| #24923271 | 2 |
| #407×C167 | 2 |
| #3092 | 167 |