Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24923814 | C2 | semidirect |
| 2. #24923673 | C2 | semidirect |
| 3. #24923644 | C2 | semidirect |
| 4. #24923614 | C2 | semidirect |
| 5. #24923505 | C2 | semidirect |
| 6. #24923503 | C2 | semidirect |
| 7. D8×Dic167 | C2 | semidirect |
| 8. #24923351 | C2 | semidirect |
| 9. #24923349 | C2 | semidirect |
| 10. C2×C8×Dic167 | C2 | semidirect |
| 11. #466×C167 | C2 | semidirect |
| 82. C2×Dic167 | D8 | semidirect |
| 89. C167⋊C8 | #41 | semidirect |
| 101. C8×C167 | #41 | semidirect |
| 127. C167 | #3169 | semidirect |
| 135. #466 | D167 | semidirect |
| 229. C8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923814 | 2 |
| #24923673 | 2 |
| #24923644 | 2 |
| #24923614 | 2 |
| #24923505 | 2 |
| #24923503 | 2 |
| D8×Dic167 | 2 |
| #24923351 | 2 |
| #24923349 | 2 |
| C2×C8×Dic167 | 2 |
| #466×C167 | 2 |
| #3169 | 167 |