Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic167 | C2 | semidirect |
| 3. #24923602 | C2 | semidirect |
| 5. #24923574 | C2 | semidirect |
| 6. #24923493 | C2 | semidirect |
| 8. #24923376 | C2 | semidirect |
| 9. #24923372 | C2 | semidirect |
| 10. #24923323 | C2 | semidirect |
| 11. #451×C167 | C2 | semidirect |
| 131. C167 | #3117 | semidirect |
| 139. #451 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923805 | 2 |
| C2×Q8×Dic167 | 2 |
| #24923602 | 2 |
| #24923588 | 2 |
| #24923574 | 2 |
| #24923493 | 2 |
| #24923408 | 2 |
| #24923376 | 2 |
| #24923372 | 2 |
| #24923323 | 2 |
| #451×C167 | 2 |
| #3117 | 167 |