Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 182 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. Q8×#1057 | C2 | semidirect |
| 3. #11719080 | C2 | semidirect |
| 28. #6118 | Q8 | direct (N × H) |
| 38. Q8×C13 | M16 | semidirect |
| 51. #1057 | C2×Q8 | semidirect |
| 102. C13 | Q8×M16 | semidirect |
| 105. Q8 | #6118 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D13 | 2 |
| Q8×#1057 | 2 |
| #11719080 | 2 |
| #11719052 | 2 |
| C4×#6118 | 2 |
| Q8×M16 | 13 |