Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D167 | C2 | semidirect |
| 2. C2×#19128840 | C2 | semidirect |
| 3. #24923835 | C2 | semidirect |
| 4. #24923523 | C2 | semidirect |
| 5. #24923522 | C2 | semidirect |
| 6. #24923519 | C2 | semidirect |
| 7. #24923504 | C2 | semidirect |
| 8. #24923503 | C2 | semidirect |
| 9. #24923304 | C2 | semidirect |
| 10. #24923272 | C2 | semidirect |
| 11. #469×C167 | C2 | semidirect |
| 19. C2×#14581933 | C22 | semidirect |
| 20. C22×C167⋊C8 | C22 | semidirect |
| 22. C2×C8×D167 | C22 | semidirect |
| 25. #19128807 | C22 | semidirect |
| 26. #19128806 | C22 | semidirect |
| 27. #19128803 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. #19128764 | C22 | semidirect |
| 33. #19128754 | C22 | semidirect |
| 34. #19128753 | C22 | semidirect |
| 35. #19128752 | C22 | semidirect |
| 37. C2×M16×C167 | C22 | semidirect |
| 38. #121×C167 | C22 | semidirect |
| 39. #106×C167 | C22 | semidirect |
| 40. #102×C167 | C22 | semidirect |
| 65. C8×D167 | D4 | semidirect |
| 146. C167 | #3058 | semidirect |
| 154. #469 | D167 | semidirect |
| 168. C2×M16 | C2×D167 | semidirect |
| 177. #121 | C2×D167 | semidirect |
| 183. #106 | C2×D167 | semidirect |
| 187. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D167 | 2 |
| C2×#19128840 | 2 |
| #24923835 | 2 |
| #24923523 | 2 |
| #24923522 | 2 |
| #24923519 | 2 |
| #24923504 | 2 |
| #24923503 | 2 |
| #24923304 | 2 |
| #24923272 | 2 |
| #469×C167 | 2 |
| #3058 | 167 |