Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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×Dic26 | C2 | semidirect |
| 3. #11718736 | C2 | semidirect |
| 4. #11718731 | C2 | semidirect |
| 5. Q8×#1055 | C2 | semidirect |
| 6. C4×#6105 | C2 | semidirect |
| 7. #11718669 | C2 | semidirect |
| 45. Q8×C13 | SD16 | semidirect |
| 59. Dic26 | #41 | semidirect |
| 119. C13 | #3362 | semidirect |
| 124. Q8 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| Q8×Dic26 | 2 |
| #11718736 | 2 |
| #11718731 | 2 |
| Q8×#1055 | 2 |
| C4×#6105 | 2 |
| #11718669 | 2 |
| #3362 | 13 |