Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 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. C2×#88155 | C2 | semidirect |
| 3. C2×C4×C8×C13 | C2 | semidirect |
| 4. C2×#88059 | C2 | semidirect |
| 5. C2×#88045 | C2 | semidirect |
| 6. #11718361 | C2 | direct (N × H) |
| 12. C2×Dic52 | C4 | semidirect |
| 13. #88158 | C4 | semidirect |
| 15. C2×D104 | C4 | semidirect |
| 16. C2×#6095 | C4 | semidirect |
| 18. #88155 | C22 | semidirect |
| 21. C4×C8×C13 | C22 | semidirect |
| 22. #88059 | C22 | semidirect |
| 23. #88045 | C22 | semidirect |
| 47. Dic52 | C2×C4 | semidirect |
| 48. D104 | C2×C4 | semidirect |
| 49. #6095 | C2×C4 | semidirect |
| 82. C2×C4×C8 | D13 | semidirect |
| 111. C4×C8 | C2×D13 | semidirect |
| 114. C2×C13 | #443 | semidirect |
| 145. C13 | C2×#443 | semidirect |
| 185. C2 | #11718361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| C2×#88155 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#88059 | 2 |
| C2×#88045 | 2 |
| #11718361 | 2 |
| C2×#443 | 13 |