Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923940 | C2 | semidirect |
| 2. D4×Dic334 | C2 | semidirect |
| 3. #24923616 | C2 | semidirect |
| 4. #24923614 | C2 | semidirect |
| 5. #24923549 | C2 | semidirect |
| 6. #24923548 | C2 | semidirect |
| 7. #24923464 | C2 | semidirect |
| 8. #24923462 | C2 | semidirect |
| 9. C8×Dic334 | C2 | semidirect |
| 10. #24923349 | C2 | semidirect |
| 11. C4×D8×C167 | C2 | semidirect |
| 78. Dic334 | D8 | semidirect |
| 96. D4×C167 | #41 | semidirect |
| 131. C167 | #3358 | semidirect |
| 143. C4×D8 | D167 | semidirect |
| 222. D4 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923940 | 2 |
| D4×Dic334 | 2 |
| #24923616 | 2 |
| #24923614 | 2 |
| #24923549 | 2 |
| #24923548 | 2 |
| #24923464 | 2 |
| #24923462 | 2 |
| C8×Dic334 | 2 |
| #24923349 | 2 |
| C4×D8×C167 | 2 |
| #3358 | 167 |