Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19128863 | C2 | semidirect |
| 2. C2×#19128862 | C2 | semidirect |
| 4. C22×#14581940 | C2 | semidirect |
| 5. #24923845 | C2 | semidirect |
| 6. #24923664 | C2 | semidirect |
| 7. #24923661 | C2 | semidirect |
| 8. #24923651 | C2 | semidirect |
| 9. #24923648 | C2 | semidirect |
| 10. #24923225 | C2 | semidirect |
| 11. #536×C167 | C2 | semidirect |
| 143. C167 | #3156 | semidirect |
| 150. #536 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| C2×#19128862 | 2 |
| C2×#19128852 | 2 |
| C22×#14581940 | 2 |
| #24923845 | 2 |
| #24923664 | 2 |
| #24923661 | 2 |
| #24923651 | 2 |
| #24923648 | 2 |
| #24923225 | 2 |
| #536×C167 | 2 |
| #3156 | 167 |