Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
| 3. #24923582 | C2 | semidirect |
| 4. #24923563 | C2 | semidirect |
| 5. #24923468 | C2 | semidirect |
| 6. #24923410 | C2 | semidirect |
| 7. #24923407 | C2 | semidirect |
| 8. #24923368 | C2 | semidirect |
| 9. #24923366 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #480×C167 | C2 | semidirect |
| 86. Dic334 | #41 | semidirect |
| 140. C167 | #3112 | semidirect |
| 145. #480 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923814 | 2 |
| C2×#19128797 | 2 |
| #24923582 | 2 |
| #24923563 | 2 |
| #24923468 | 2 |
| #24923410 | 2 |
| #24923407 | 2 |
| #24923368 | 2 |
| #24923366 | 2 |
| #24923323 | 2 |
| #480×C167 | 2 |
| #3112 | 167 |