Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×#88062 | C2 | semidirect |
| 5. #11718659 | C2 | semidirect |
| 6. C13×#344 | C2 | semidirect |
| 7. #11718151 | C2 | semidirect |
| 17. #88161 | C4 | semidirect |
| 18. #88161 | C4 | semidirect |
| 94. #344 | D13 | semidirect |
| 166. C13 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| #11718800 | 2 |
| C2×#88062 | 2 |
| #11718666 | 2 |
| #11718659 | 2 |
| C13×#344 | 2 |
| #11718151 | 2 |
| #1814 | 13 |