Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C2×#19128862 | C2 | semidirect |
| 2. C2×#19128857 | C2 | semidirect |
| 3. C22×#14581939 | C2 | semidirect |
| 4. #24923840 | C2 | semidirect |
| 5. #24923833 | C2 | semidirect |
| 6. #24923662 | C2 | semidirect |
| 7. #24923657 | C2 | semidirect |
| 8. #24923650 | C2 | semidirect |
| 9. #24923640 | C2 | semidirect |
| 10. #24923224 | C2 | semidirect |
| 11. C2×#135×C167 | C2 | semidirect |
| 16. C2×#14581940 | C22 | semidirect |
| 20. C2×#14581938 | C22 | semidirect |
| 24. #19128830 | C22 | semidirect |
| 27. #19128819 | C22 | semidirect |
| 33. #19128742 | C22 | semidirect |
| 34. C8×Dic167 | C22 | semidirect |
| 38. C2×Q16×C167 | C22 | semidirect |
| 39. C2×SD16×C167 | C22 | semidirect |
| 40. C2×SD16×C167 | C22 | semidirect |
| 41. C2×D8×C167 | C22 | semidirect |
| 60. #14581934 | D4 | semidirect |
| 85. C2×C8×C167 | D4 | semidirect |
| 148. C167 | #3154 | semidirect |
| 152. C2×#135 | D167 | semidirect |
| 169. C2×Q16 | C2×D167 | semidirect |
| 175. C2×SD16 | C2×D167 | semidirect |
| 176. C2×SD16 | C2×D167 | semidirect |
| 178. C2×D8 | C2×D167 | semidirect |
| 228. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128862 | 2 |
| C2×#19128857 | 2 |
| C22×#14581939 | 2 |
| #24923840 | 2 |
| #24923833 | 2 |
| #24923662 | 2 |
| #24923657 | 2 |
| #24923650 | 2 |
| #24923640 | 2 |
| #24923224 | 2 |
| C2×#135×C167 | 2 |
| #3154 | 167 |