Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1048 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 581 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 |
|---|---|---|
| 3. #11719275 | C2 | direct (N × H) |
| 21. C2×Q8×C13 | Q8 | semidirect |
| 39. Q8×C13 | C2×Q8 | semidirect |
| 80. C2×C13 | #557 | semidirect |
| 86. C2×Q8 | Dic26 | semidirect |
| 100. C13 | C2×#557 | semidirect |
| 103. Q8 | C2×Dic26 | semidirect |
| 123. C2 | #11719275 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C13 | 2 |
| C2×Q8×Dic13 | 2 |
| #11719275 | 2 |
| C2×#88144 | 2 |
| C2×#88123 | 2 |
| C2×C4×Dic26 | 2 |
| C2×#557 | 13 |