Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88144 | C2 | semidirect |
| 5. C2×#88058 | C2 | semidirect |
| 6. C2×#88054 | C2 | semidirect |
| 7. C2×#88048 | C2 | semidirect |
| 8. #11718427 | C2 | direct (N × H) |
| 23. #88144 | C22 | semidirect |
| 26. #88058 | C22 | semidirect |
| 27. #88054 | C22 | semidirect |
| 28. #88048 | C22 | semidirect |
| 128. C2×C13 | #478 | semidirect |
| 160. C13 | C2×#478 | semidirect |
| 203. C2 | #11718427 | 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×#88144 | 2 |
| C2×C13×#102 | 2 |
| C2×#88072 | 2 |
| C2×#88058 | 2 |
| C2×#88054 | 2 |
| C2×#88048 | 2 |
| #11718427 | 2 |
| C2×#478 | 13 |