Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. #11719532 | C2 | semidirect |
| 3. #11718893 | C2 | semidirect |
| 4. #11718845 | C2 | semidirect |
| 5. SD16×Dic13 | C2 | semidirect |
| 6. #11718813 | C2 | semidirect |
| 7. C2×#88057 | C2 | semidirect |
| 8. #11718762 | C2 | semidirect |
| 10. C13×#135 | C4 | semidirect |
| 30. C13×#41 | C2×C4 | semidirect |
| 38. C13×Q16 | C2×C4 | semidirect |
| 39. C13×SD16 | C2×C4 | semidirect |
| 40. C13×D8 | C2×C4 | semidirect |
| 41. C2×C8×C13 | C2×C4 | semidirect |
| 96. #135 | Dic13 | semidirect |
| 120. #41 | C2×Dic13 | semidirect |
| 128. Q16 | C2×Dic13 | semidirect |
| 129. SD16 | C2×Dic13 | semidirect |
| 130. D8 | C2×Dic13 | semidirect |
| 133. C2×C8 | C2×Dic13 | semidirect |
| 144. C13 | #2952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #11719532 | 2 |
| #11718893 | 2 |
| #11718845 | 2 |
| SD16×Dic13 | 2 |
| #11718813 | 2 |
| C2×#88057 | 2 |
| #11718762 | 2 |
| #2952 | 13 |