Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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×#88162 | C2 | semidirect |
| 2. C2×#88158 | C2 | semidirect |
| 3. C22×D104 | C2 | semidirect |
| 4. #11719230 | C2 | semidirect |
| 5. C13×#405 | C2 | semidirect |
| 6. #11718373 | C2 | semidirect |
| 7. #11718357 | C2 | semidirect |
| 8. #11718356 | C2 | semidirect |
| 15. C2×Dic52 | C22 | semidirect |
| 20. C2×D104 | C22 | semidirect |
| 21. C2×D104 | C22 | semidirect |
| 22. C2×#6095 | C22 | semidirect |
| 23. C2×#6095 | C22 | semidirect |
| 26. #88129 | C22 | semidirect |
| 27. #88128 | C22 | semidirect |
| 28. C13×#97 | C22 | semidirect |
| 29. C4×C8×C13 | C22 | semidirect |
| 43. C13×M16 | D4 | semidirect |
| 44. C2×C8×C13 | D4 | semidirect |
| 91. #405 | D13 | semidirect |
| 124. #97 | C2×D13 | semidirect |
| 125. C4×C8 | C2×D13 | semidirect |
| 151. M16 | D52 | semidirect |
| 152. C2×C8 | D52 | semidirect |
| 160. C13 | #3155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88162 | 2 |
| C2×#88158 | 2 |
| C22×D104 | 2 |
| #11719230 | 2 |
| C13×#405 | 2 |
| #11718373 | 2 |
| #11718357 | 2 |
| #11718356 | 2 |
| #3155 | 13 |