Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11718891 | C2 | semidirect |
| 4. C2×#88075 | C2 | semidirect |
| 6. #11718143 | C2 | semidirect |
| 7. #11718142 | C2 | semidirect |
| 13. C2×C13×SD16 | C4 | semidirect |
| 32. C2×Q8×C13 | C2×C4 | semidirect |
| 51. C2×C8×C13 | C2×C4 | semidirect |
| 100. C2×Dic13 | SD16 | semidirect |
| 138. C2×SD16 | Dic13 | semidirect |
| 165. C2×Q8 | C2×Dic13 | semidirect |
| 187. C2×C8 | C2×Dic13 | semidirect |
| 195. C13 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| C2×D4×Dic13 | 2 |
| #11718891 | 2 |
| C2×#88075 | 2 |
| C2×#88072 | 2 |
| #11718143 | 2 |
| #11718142 | 2 |
| #1877 | 13 |