Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19128851 | C2 | semidirect |
| 2. #24923918 | C2 | semidirect |
| 3. #24923647 | C2 | semidirect |
| 4. #24923510 | C2 | semidirect |
| 5. #24923507 | C2 | semidirect |
| 6. #24923472 | C2 | semidirect |
| 7. #24923431 | C2 | semidirect |
| 8. #24923428 | C2 | semidirect |
| 9. D8×Dic167 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. C2×#135×C167 | C2 | semidirect |
| 76. D8×C167 | D4 | semidirect |
| 129. Dic167 | #135 | semidirect |
| 136. C167 | #3283 | semidirect |
| 139. C2×#135 | D167 | semidirect |
| 198. D8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128851 | 2 |
| #24923918 | 2 |
| #24923647 | 2 |
| #24923510 | 2 |
| #24923507 | 2 |
| #24923472 | 2 |
| #24923431 | 2 |
| #24923428 | 2 |
| D8×Dic167 | 2 |
| C8×C22⋊D167 | 2 |
| C2×#135×C167 | 2 |
| #3283 | 167 |