Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#88202 | C2 | semidirect |
| 3. #11718897 | C2 | semidirect |
| 4. #11718858 | C2 | semidirect |
| 5. #11718857 | C2 | semidirect |
| 6. #11718786 | C2 | semidirect |
| 7. #11718783 | C2 | semidirect |
| 9. C13×#137 | C4 | semidirect |
| 10. C13×AGL(1,ℤ/8) | C4 | semidirect |
| 15. #88202 | C22 | semidirect |
| 16. #88202 | C22 | semidirect |
| 22. #88077 | C22 | semidirect |
| 23. #88059 | C22 | semidirect |
| 24. #88055 | C22 | semidirect |
| 25. C8×Dic13 | C22 | semidirect |
| 94. #137 | Dic13 | semidirect |
| 95. AGL(1,ℤ/8) | Dic13 | semidirect |
| 143. C13 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#575 | 2 |
| C2×#88202 | 2 |
| #11718897 | 2 |
| #11718858 | 2 |
| #11718857 | 2 |
| #11718786 | 2 |
| #11718783 | 2 |
| #2955 | 13 |