Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 8. #11718517 | C2 | direct (N × H) |
| 38. C2×C8×C13 | Q8 | semidirect |
| 53. C2×#1055 | Q8 | semidirect |
| 74. C8×C13 | C2×Q8 | semidirect |
| 75. #1055 | C2×Q8 | semidirect |
| 117. C2×C13 | #501 | semidirect |
| 132. C2×C8 | Dic26 | semidirect |
| 147. C13 | C2×#501 | semidirect |
| 167. C8 | C2×Dic26 | semidirect |
| 181. C2 | #11718517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88144 | 2 |
| C2×#88142 | 2 |
| C2×C13×#106 | 2 |
| C2×#88058 | 2 |
| C2×#88055 | 2 |
| C2×#88048 | 2 |
| C2×#88047 | 2 |
| #11718517 | 2 |
| C2×#501 | 13 |