Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×#19128797 | C2 | semidirect |
| 4. #24923575 | C2 | semidirect |
| 5. #24923494 | C2 | semidirect |
| 6. #24923424 | C2 | semidirect |
| 8. #24923373 | C2 | semidirect |
| 9. #24923368 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #484×C167 | C2 | semidirect |
| 131. C167 | #3117 | semidirect |
| 135. #484 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923805 | 2 |
| C2×#19128797 | 2 |
| #24923587 | 2 |
| #24923575 | 2 |
| #24923494 | 2 |
| #24923424 | 2 |
| #24923410 | 2 |
| #24923373 | 2 |
| #24923368 | 2 |
| #24923323 | 2 |
| #484×C167 | 2 |
| #3117 | 167 |