Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923989 | C2 | semidirect |
| 2. #24923940 | C2 | semidirect |
| 3. #24923657 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923483 | C2 | semidirect |
| 6. #24923474 | C2 | semidirect |
| 7. #24923468 | C2 | semidirect |
| 8. #24923464 | C2 | semidirect |
| 9. #24923399 | C2 | semidirect |
| 10. #24923368 | C2 | semidirect |
| 11. C4×D8×C167 | C2 | semidirect |
| 106. C8×C167 | #41 | semidirect |
| 132. C167 | #3397 | semidirect |
| 144. C4×D8 | D167 | semidirect |
| 239. C8 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923989 | 2 |
| #24923940 | 2 |
| #24923657 | 2 |
| #24923642 | 2 |
| #24923483 | 2 |
| #24923474 | 2 |
| #24923468 | 2 |
| #24923464 | 2 |
| #24923399 | 2 |
| #24923368 | 2 |
| C4×D8×C167 | 2 |
| #3397 | 167 |