Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 157 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. #24923207 | C2 | semidirect |
| 3. #24923204 | C2 | semidirect |
| 4. #24923200 | C2 | semidirect |
| 5. #24923197 | C2 | semidirect |
| 6. #24923195 | C2 | semidirect |
| 8. C4×Dic167⋊C4 | C2 | semidirect |
| 9. C4×(C2×D167)⋊C4 | C2 | semidirect |
| 10. C4×C22⋊Dic167 | C2 | semidirect |
| 11. C2×#117×C167 | C2 | semidirect |
| 137. C167 | #2395 | semidirect |
| 140. C2×#117 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D167 | 2 |
| #24923207 | 2 |
| #24923204 | 2 |
| #24923200 | 2 |
| #24923197 | 2 |
| #24923195 | 2 |
| #24923184 | 2 |
| C4×Dic167⋊C4 | 2 |
| C4×(C2×D167)⋊C4 | 2 |
| C4×C22⋊Dic167 | 2 |
| C2×#117×C167 | 2 |
| #2395 | 167 |