Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #24923679 | C2 | semidirect |
| 4. #24923678 | C2 | semidirect |
| 5. #24923675 | C2 | semidirect |
| 6. #24923670 | C2 | semidirect |
| 7. #24923669 | C2 | semidirect |
| 11. #501×C167 | C2 | semidirect |
| 49. #14581933 | Q8 | semidirect |
| 121. C167 | #3166 | semidirect |
| 128. #501 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923824 | 2 |
| #125×D167 | 2 |
| #24923679 | 2 |
| #24923678 | 2 |
| #24923675 | 2 |
| #24923670 | 2 |
| #24923669 | 2 |
| #24923310 | 2 |
| #24923308 | 2 |
| #24923221 | 2 |
| #501×C167 | 2 |
| #3166 | 167 |