Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 6. #11718640 | C2 | direct (N × H) |
| 28. C22×C4×C13 | Q8 | semidirect |
| 37. C22×Dic13 | Q8 | semidirect |
| 61. C2×C4×C13 | C2×Q8 | semidirect |
| 69. C2×Dic13 | C2×Q8 | semidirect |
| 106. C2×C13 | #395 | semidirect |
| 129. C22×C4 | Dic26 | semidirect |
| 136. C13 | C2×#395 | semidirect |
| 160. C2×C4 | C2×Dic26 | semidirect |
| 177. C2 | #11718640 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic26 | 2 |
| C22×C13×C4⋊C4 | 2 |
| C22×#6101 | 2 |
| C2×#88071 | 2 |
| #11718640 | 2 |
| C2×#395 | 13 |