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 |
|---|---|---|
| 1. C2×#88163 | C2 | semidirect |
| 3. C2×#88129 | C2 | semidirect |
| 4. C4×#6127 | C2 | semidirect |
| 5. C13×#423 | C2 | semidirect |
| 6. #11718792 | C2 | semidirect |
| 7. #11718781 | C2 | semidirect |
| 8. #11718506 | C2 | semidirect |
| 9. #11718505 | C2 | semidirect |
| 21. C2×Dic52 | C22 | semidirect |
| 24. C2×#6095 | C22 | semidirect |
| 28. C4×D52 | C22 | semidirect |
| 31. C4×Dic26 | C22 | semidirect |
| 32. C13×C4⋊C8 | C22 | semidirect |
| 34. #88056 | C22 | semidirect |
| 111. #423 | D13 | semidirect |
| 152. C4⋊C8 | C2×D13 | 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×#88163 | 2 |
| C2×#88162 | 2 |
| C2×#88129 | 2 |
| C4×#6127 | 2 |
| C13×#423 | 2 |
| #11718792 | 2 |
| #11718781 | 2 |
| #11718506 | 2 |
| #11718505 | 2 |
| #3040 | 13 |