Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24923999 | C2 | semidirect |
| 3. #24923614 | C2 | semidirect |
| 4. #24923557 | C2 | semidirect |
| 5. #24923556 | C2 | semidirect |
| 6. #24923468 | C2 | semidirect |
| 7. #24923466 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 9. #24923360 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. #486×C167 | C2 | semidirect |
| 77. Dic334 | SD16 | semidirect |
| 78. Dic334 | #41 | semidirect |
| 125. C167 | #3362 | semidirect |
| 130. #486 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923999 | 2 |
| #24923939 | 2 |
| #24923614 | 2 |
| #24923557 | 2 |
| #24923556 | 2 |
| #24923468 | 2 |
| #24923466 | 2 |
| C8×Dic334 | 2 |
| #24923360 | 2 |
| C4×#14581939 | 2 |
| #486×C167 | 2 |
| #3362 | 167 |