Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11718767 | C2 | semidirect |
| 3. C2×#88052 | C2 | semidirect |
| 4. #11718158 | C2 | semidirect |
| 8. C13×#135 | C4 | semidirect |
| 10. C2×C13×Q16 | C4 | semidirect |
| 12. C2×C13×D8 | C4 | semidirect |
| 16. #88057 | C22 | semidirect |
| 18. #88052 | C22 | semidirect |
| 87. #135 | Dic13 | semidirect |
| 89. C2×Q16 | Dic13 | semidirect |
| 91. C2×D8 | Dic13 | semidirect |
| 129. C13 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #11718767 | 2 |
| C2×#88052 | 2 |
| #11718158 | 2 |
| #2145 | 13 |