Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. #24923881 | C2 | semidirect |
| 3. #24923671 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923638 | C2 | semidirect |
| 6. #24923634 | C2 | semidirect |
| 7. #24923515 | C2 | semidirect |
| 8. #24923498 | C2 | semidirect |
| 9. #24923371 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. #405×C167 | C2 | semidirect |
| 108. C167 | #3174 | semidirect |
| 120. #405 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923881 | 2 |
| #24923874 | 2 |
| #24923671 | 2 |
| #24923642 | 2 |
| #24923638 | 2 |
| #24923634 | 2 |
| #24923515 | 2 |
| #24923498 | 2 |
| #24923371 | 2 |
| C4×#14581939 | 2 |
| #405×C167 | 2 |
| #3174 | 167 |