Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 8. #11718515 | C2 | direct (N × H) |
| 40. C2×Dic26 | Q8 | semidirect |
| 78. Dic26 | C2×Q8 | semidirect |
| 122. C2×C13 | #475 | semidirect |
| 154. C13 | C2×#475 | semidirect |
| 191. C2 | #11718515 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88142 | 2 |
| C2×#88141 | 2 |
| C2×C13×#106 | 2 |
| C2×#88056 | 2 |
| C2×#88054 | 2 |
| C2×#88050 | 2 |
| C2×#88048 | 2 |
| #11718515 | 2 |
| C2×#475 | 13 |