Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 5. #24923552 | C2 | semidirect |
| 6. #24923477 | C2 | semidirect |
| 8. #24923376 | C2 | semidirect |
| 9. #24923373 | C2 | semidirect |
| 127. C167 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923821 | 2 |
| C2×Q8×Dic167 | 2 |
| #24923600 | 2 |
| #24923597 | 2 |
| #24923552 | 2 |
| #24923477 | 2 |
| #24923425 | 2 |
| #24923376 | 2 |
| #24923373 | 2 |
| #24923323 | 2 |
| #451×C167 | 2 |
| #3113 | 167 |