Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11718754 | C2 | semidirect |
| 4. #11718753 | C2 | semidirect |
| 5. #11718742 | C2 | semidirect |
| 6. #11718739 | C2 | semidirect |
| 8. C4×#6107 | C2 | semidirect |
| 74. C2×C4×C13 | Q16 | semidirect |
| 170. C13 | #3170 | semidirect |
| 182. C2×C4 | #6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| #11719175 | 2 |
| #11718754 | 2 |
| #11718753 | 2 |
| #11718742 | 2 |
| #11718739 | 2 |
| #11718712 | 2 |
| C4×#6107 | 2 |
| C2×C4×#1055 | 2 |
| #3170 | 13 |