Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. C2×#88142 | C2 | semidirect |
| 5. C2×#88058 | C2 | semidirect |
| 6. C2×#88054 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 8. #11718420 | C2 | direct (N × H) |
| 23. #88142 | C22 | semidirect |
| 26. #88058 | C22 | semidirect |
| 27. #88054 | C22 | semidirect |
| 28. #88047 | C22 | semidirect |
| 32. C2×D4×C13 | Q8 | semidirect |
| 66. D4×C13 | C2×Q8 | semidirect |
| 130. C2×C13 | #474 | semidirect |
| 139. C2×D4 | Dic26 | semidirect |
| 163. C13 | C2×#474 | semidirect |
| 172. D4 | C2×Dic26 | semidirect |
| 207. C2 | #11718420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic13 | 2 |
| C2×#88142 | 2 |
| C2×C13×#102 | 2 |
| C2×#88072 | 2 |
| C2×#88058 | 2 |
| C2×#88054 | 2 |
| C2×#88047 | 2 |
| #11718420 | 2 |
| C2×#474 | 13 |