Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 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×#14581950 | C2 | semidirect |
| 2. C2×#19128858 | C2 | semidirect |
| 3. #24923412 | C2 | semidirect |
| 4. #24923407 | C2 | semidirect |
| 5. #24923402 | C2 | semidirect |
| 6. #24923268 | C2 | semidirect |
| 7. #24923233 | C2 | semidirect |
| 8. C2×#121×C167 | C2 | semidirect |
| 13. C2×#14581950 | C22 | semidirect |
| 14. C22×Dic334 | C22 | semidirect |
| 15. C22×D668 | C22 | semidirect |
| 19. C2×#14581938 | C22 | semidirect |
| 20. C2×#14581935 | C22 | semidirect |
| 21. C2×#14581934 | C22 | semidirect |
| 22. #19128755 | C22 | semidirect |
| 23. #19128752 | C22 | semidirect |
| 24. C22⋊(C167⋊C8) | C22 | semidirect |
| 25. C22⋊(C167⋊C8) | C22 | semidirect |
| 27. C22×D4×C167 | C22 | semidirect |
| 32. #121×C167 | C22 | semidirect |
| 33. C2×C4⋊C4×C167 | C22 | semidirect |
| 41. #14581950 | D4 | semidirect |
| 85. Dic334 | C2×D4 | semidirect |
| 88. D668 | C2×D4 | semidirect |
| 135. C22×C167 | AGL(1,ℤ/8) | semidirect |
| 155. C167 | #3006 | semidirect |
| 159. C2×#121 | D167 | semidirect |
| 174. C22×D4 | C2×D167 | semidirect |
| 184. #121 | C2×D167 | semidirect |
| 185. C2×C4⋊C4 | C2×D167 | semidirect |
| 295. C22 | #19128858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581950 | 2 |
| C2×#19128858 | 2 |
| #24923412 | 2 |
| #24923407 | 2 |
| #24923402 | 2 |
| #24923268 | 2 |
| #24923233 | 2 |
| C2×#121×C167 | 2 |
| #3006 | 167 |