Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. #41×Dic13 | C2 | semidirect |
| 3. C2×#88205 | C2 | semidirect |
| 4. C2×#88190 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. #11718827 | C2 | semidirect |
| 7. #11718814 | C2 | semidirect |
| 8. #11718781 | C2 | semidirect |
| 9. #11718779 | C2 | semidirect |
| 19. Q8×Dic13 | C22 | semidirect |
| 20. C2×#6107 | C22 | semidirect |
| 25. D4×Dic13 | C22 | semidirect |
| 26. C2×#6105 | C22 | semidirect |
| 33. #88056 | C22 | semidirect |
| 34. #88054 | C22 | semidirect |
| 198. C13 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×AGL(1,ℤ/8) | 2 |
| #41×Dic13 | 2 |
| C2×#88205 | 2 |
| C2×#88190 | 2 |
| #11718876 | 2 |
| #11718827 | 2 |
| #11718814 | 2 |
| #11718781 | 2 |
| #11718779 | 2 |
| #3040 | 13 |