Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11718685 | C2 | semidirect |
| 4. Q8⋊#1055 | C2 | semidirect |
| 6. #11718050 | C2 | semidirect |
| 7. #11718047 | C2 | semidirect |
| 56. C8×C13 | M16 | semidirect |
| 118. C13 | #1592 | semidirect |
| 138. C8 | #6099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×SD16 | 2 |
| #11718685 | 2 |
| #11718673 | 2 |
| Q8⋊#1055 | 2 |
| D4⋊#1055 | 2 |
| #11718050 | 2 |
| #11718047 | 2 |
| #1592 | 13 |