Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 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. C2×#19128858 | C2 | semidirect |
| 2. #24923819 | C2 | semidirect |
| 3. #24923484 | C2 | semidirect |
| 4. #24923474 | C2 | semidirect |
| 5. #24923464 | C2 | semidirect |
| 6. #24923293 | C2 | semidirect |
| 7. #24923268 | C2 | semidirect |
| 8. C2×C4×D4×C167 | C2 | semidirect |
| 14. #19128832 | C22 | semidirect |
| 15. #19128829 | C22 | semidirect |
| 16. #19128820 | C22 | semidirect |
| 21. C4⋊(C167⋊C8) | C22 | semidirect |
| 22. C4⋊(C167⋊C8) | C22 | semidirect |
| 23. #19128755 | C22 | semidirect |
| 24. #19128752 | C22 | semidirect |
| 53. C2×D4×C167 | D4 | semidirect |
| 119. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 129. C167 | #3036 | semidirect |
| 133. C2×C4×D4 | D167 | semidirect |
| 174. C2×D4 | D668 | semidirect |
| 250. C4 | #19128858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128858 | 2 |
| #24923819 | 2 |
| #24923484 | 2 |
| #24923474 | 2 |
| #24923464 | 2 |
| #24923293 | 2 |
| #24923268 | 2 |
| C2×C4×D4×C167 | 2 |
| #3036 | 167 |