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×#14581949 | C2 | semidirect |
| 2. C2×#19128862 | C2 | semidirect |
| 3. #24923776 | C2 | semidirect |
| 4. #24923428 | C2 | semidirect |
| 5. #24923411 | C2 | semidirect |
| 6. #24923279 | C2 | semidirect |
| 7. #24923274 | C2 | semidirect |
| 8. #24923232 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 19. C2×#14581940 | C22 | semidirect |
| 20. C2×#14581938 | C22 | semidirect |
| 23. #19128808 | C22 | semidirect |
| 24. #19128803 | C22 | semidirect |
| 28. #19128757 | C22 | semidirect |
| 29. #19128753 | C22 | semidirect |
| 30. (C2×D167)⋊C8 | C22 | semidirect |
| 34. C2×SD16×C167 | C22 | semidirect |
| 35. C2×D8×C167 | C22 | semidirect |
| 43. C2×Dic334 | D4 | semidirect |
| 73. C2×D4×C167 | D4 | semidirect |
| 145. C167 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D167 | semidirect |
| 170. C2×SD16 | C2×D167 | semidirect |
| 171. C2×D8 | C2×D167 | semidirect |
| 201. C2×D4 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581949 | 2 |
| C2×#19128862 | 2 |
| #24923776 | 2 |
| #24923428 | 2 |
| #24923411 | 2 |
| #24923279 | 2 |
| #24923274 | 2 |
| #24923232 | 2 |
| C2×AGL(1,ℤ/8)×C167 | 2 |
| #3005 | 167 |