Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #24924005 | C2 | semidirect |
| 2. #24923939 | C2 | semidirect |
| 3. #24923657 | C2 | semidirect |
| 4. #24923482 | C2 | semidirect |
| 5. #24923466 | C2 | semidirect |
| 6. #24923462 | C2 | semidirect |
| 7. #24923461 | C2 | semidirect |
| 8. #24923399 | C2 | semidirect |
| 9. #24923381 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. #493×C167 | C2 | semidirect |
| 108. C8×C167 | #41 | semidirect |
| 134. C167 | #3399 | semidirect |
| 139. #493 | D167 | semidirect |
| 243. C8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924005 | 2 |
| #24923939 | 2 |
| #24923657 | 2 |
| #24923482 | 2 |
| #24923466 | 2 |
| #24923462 | 2 |
| #24923461 | 2 |
| #24923399 | 2 |
| #24923381 | 2 |
| C4×#14581939 | 2 |
| #493×C167 | 2 |
| #3399 | 167 |