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×#19128857 | C2 | semidirect |
| 3. #24923776 | C2 | semidirect |
| 4. #24923430 | C2 | semidirect |
| 5. #24923413 | C2 | semidirect |
| 6. #24923278 | C2 | semidirect |
| 7. #24923275 | C2 | semidirect |
| 8. #24923232 | C2 | semidirect |
| 9. C2×#137×C167 | C2 | semidirect |
| 19. C2×#14581937 | C22 | semidirect |
| 20. C2×#14581935 | C22 | semidirect |
| 23. #19128808 | C22 | semidirect |
| 24. #19128803 | C22 | semidirect |
| 28. #19128756 | C22 | semidirect |
| 29. #19128754 | C22 | semidirect |
| 30. (C2×D167)⋊C8 | C22 | semidirect |
| 34. C2×Q16×C167 | C22 | semidirect |
| 35. C2×SD16×C167 | C22 | semidirect |
| 46. C2×D668 | D4 | semidirect |
| 70. C2×Q8×C167 | D4 | semidirect |
| 145. C167 | #3005 | semidirect |
| 148. C2×#137 | D167 | semidirect |
| 168. C2×Q16 | C2×D167 | semidirect |
| 170. C2×SD16 | C2×D167 | semidirect |
| 192. C2×Q8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581951 | 2 |
| C2×#19128857 | 2 |
| #24923776 | 2 |
| #24923430 | 2 |
| #24923413 | 2 |
| #24923278 | 2 |
| #24923275 | 2 |
| #24923232 | 2 |
| C2×#137×C167 | 2 |
| #3005 | 167 |