Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19128855 | C2 | semidirect |
| 2. C2×#19128838 | C2 | semidirect |
| 3. #24923849 | C2 | semidirect |
| 4. #24923518 | C2 | semidirect |
| 5. #24923517 | C2 | semidirect |
| 6. #24923507 | C2 | semidirect |
| 7. #24923506 | C2 | semidirect |
| 8. #24923505 | C2 | semidirect |
| 9. #107×D167 | C2 | semidirect |
| 10. #24923269 | C2 | semidirect |
| 11. #467×C167 | C2 | semidirect |
| 65. C8×D167 | D4 | semidirect |
| 143. C167 | #3061 | semidirect |
| 151. #467 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128855 | 2 |
| C2×#19128838 | 2 |
| #24923849 | 2 |
| #24923518 | 2 |
| #24923517 | 2 |
| #24923507 | 2 |
| #24923506 | 2 |
| #24923505 | 2 |
| #107×D167 | 2 |
| #24923269 | 2 |
| #467×C167 | 2 |
| #3061 | 167 |