Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19128856 | C2 | semidirect |
| 2. #24923817 | C2 | semidirect |
| 3. C4×D4×D167 | C2 | semidirect |
| 4. #24923483 | C2 | semidirect |
| 5. #24923482 | C2 | semidirect |
| 6. #24923475 | C2 | semidirect |
| 7. #24923474 | C2 | semidirect |
| 8. #24923461 | C2 | semidirect |
| 9. #24923291 | C2 | semidirect |
| 10. #24923267 | C2 | semidirect |
| 11. #459×C167 | C2 | semidirect |
| 20. #19128832 | C22 | semidirect |
| 21. #19128819 | C22 | semidirect |
| 34. C4⋊(C167⋊C8) | C22 | semidirect |
| 35. Dic167⋊C8 | C22 | semidirect |
| 36. #19128757 | C22 | semidirect |
| 37. #19128755 | C22 | semidirect |
| 38. #19128753 | C22 | semidirect |
| 40. #127×C167 | C22 | semidirect |
| 42. C4⋊C8×C167 | C22 | semidirect |
| 43. #102×C167 | C22 | semidirect |
| 52. D4×D167 | D4 | semidirect |
| 145. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 160. C167 | #3036 | semidirect |
| 170. #459 | D167 | semidirect |
| 183. #127 | C2×D167 | semidirect |
| 200. C4⋊C8 | C2×D167 | semidirect |
| 204. #102 | C2×D167 | semidirect |
| 311. C4 | #19128856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128856 | 2 |
| #24923817 | 2 |
| C4×D4×D167 | 2 |
| #24923483 | 2 |
| #24923482 | 2 |
| #24923475 | 2 |
| #24923474 | 2 |
| #24923461 | 2 |
| #24923291 | 2 |
| #24923267 | 2 |
| #459×C167 | 2 |
| #3036 | 167 |