Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C22×Q8×D167 | C2 | semidirect |
| 2. C2×#19128865 | C2 | semidirect |
| 3. C2×#19128863 | C2 | semidirect |
| 5. #24923426 | C2 | semidirect |
| 6. #24923409 | C2 | semidirect |
| 7. #24923277 | C2 | semidirect |
| 8. #24923232 | C2 | semidirect |
| 9. #419×C167 | C2 | semidirect |
| 21. C2×Dic668 | C22 | semidirect |
| 22. C2×#14581940 | C22 | semidirect |
| 23. C2×#14581939 | C22 | semidirect |
| 24. C2×#14581937 | C22 | semidirect |
| 31. #19128755 | C22 | semidirect |
| 36. #103×C167 | C22 | semidirect |
| 44. C2×Dic334 | D4 | semidirect |
| 73. C2×Q8×C167 | D4 | semidirect |
| 127. C2×D167 | #137 | semidirect |
| 141. C167 | #3004 | semidirect |
| 150. #419 | D167 | semidirect |
| 177. #103 | C2×D167 | semidirect |
| 194. C2×Q8 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D167 | 2 |
| C2×#19128865 | 2 |
| C2×#19128863 | 2 |
| #24923781 | 2 |
| #24923426 | 2 |
| #24923409 | 2 |
| #24923277 | 2 |
| #24923232 | 2 |
| #419×C167 | 2 |
| #3004 | 167 |