Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14581951 | C2 | semidirect |
| 2. C2×#19128863 | C2 | semidirect |
| 3. C2×#19128860 | C2 | semidirect |
| 4. #24923781 | C2 | semidirect |
| 5. #24923434 | C2 | semidirect |
| 6. #24923417 | C2 | semidirect |
| 7. #24923273 | C2 | semidirect |
| 8. #24923232 | C2 | semidirect |
| 9. #419×C167 | C2 | semidirect |
| 21. C2×#14581940 | C22 | semidirect |
| 22. C2×#14581939 | C22 | semidirect |
| 23. C2×#14581937 | C22 | semidirect |
| 24. C2×D1336 | C22 | semidirect |
| 27. #19128812 | C22 | semidirect |
| 28. #19128807 | C22 | semidirect |
| 31. #19128752 | C22 | semidirect |
| 32. (C2×D167)⋊C8 | C22 | semidirect |
| 36. #103×C167 | C22 | semidirect |
| 50. C2×D668 | D4 | semidirect |
| 73. C2×Q8×C167 | D4 | semidirect |
| 145. C167 | #3005 | semidirect |
| 153. #419 | D167 | semidirect |
| 180. #103 | C2×D167 | semidirect |
| 193. C2×Q8 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581951 | 2 |
| C2×#19128863 | 2 |
| C2×#19128860 | 2 |
| #24923781 | 2 |
| #24923434 | 2 |
| #24923417 | 2 |
| #24923273 | 2 |
| #24923232 | 2 |
| #419×C167 | 2 |
| #3005 | 167 |