Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
| 2. C22×#6095 | C2 | semidirect |
| 4. #11719221 | C2 | semidirect |
| 5. C13×#424 | C2 | semidirect |
| 6. #11718792 | C2 | semidirect |
| 7. #11718774 | C2 | semidirect |
| 8. #11718509 | C2 | semidirect |
| 9. #11718506 | C2 | semidirect |
| 18. C2×Dic52 | C22 | semidirect |
| 21. C2×#6095 | C22 | semidirect |
| 28. C4×Dic26 | C22 | semidirect |
| 29. C13×C4⋊C8 | C22 | semidirect |
| 31. #88061 | C22 | semidirect |
| 32. #88056 | C22 | semidirect |
| 48. C2×Dic26 | D4 | semidirect |
| 103. #424 | D13 | semidirect |
| 140. C4⋊C8 | C2×D13 | semidirect |
| 183. C13 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| C22×#6095 | 2 |
| #11719230 | 2 |
| #11719221 | 2 |
| C13×#424 | 2 |
| #11718792 | 2 |
| #11718774 | 2 |
| #11718509 | 2 |
| #11718506 | 2 |
| #3043 | 13 |