Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128852 | C2 | semidirect |
| 2. C2×#19128840 | C2 | semidirect |
| 3. #24923850 | C2 | semidirect |
| 4. #24923847 | C2 | semidirect |
| 5. #24923526 | C2 | semidirect |
| 6. #24923521 | C2 | semidirect |
| 7. #24923501 | C2 | semidirect |
| 8. #24923497 | C2 | semidirect |
| 9. C2×#19128763 | C2 | semidirect |
| 10. #24923271 | C2 | semidirect |
| 11. #417×C167 | C2 | semidirect |
| 63. C2×C167⋊C8 | D4 | semidirect |
| 152. C167 | #3060 | semidirect |
| 164. #417 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128852 | 2 |
| C2×#19128840 | 2 |
| #24923850 | 2 |
| #24923847 | 2 |
| #24923526 | 2 |
| #24923521 | 2 |
| #24923501 | 2 |
| #24923497 | 2 |
| C2×#19128763 | 2 |
| #24923271 | 2 |
| #417×C167 | 2 |
| #3060 | 167 |