Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×C13×#131 | C2 | semidirect |
| 3. #11719530 | C2 | semidirect |
| 4. C22×#6095 | C2 | semidirect |
| 5. #11718795 | C2 | semidirect |
| 6. #11718792 | C2 | semidirect |
| 7. #11718781 | C2 | semidirect |
| 8. #11718775 | C2 | semidirect |
| 9. #11718767 | C2 | semidirect |
| 15. C2×C13×M16 | C22 | semidirect |
| 17. C22×C8×C13 | C22 | semidirect |
| 27. #88178 | C22 | semidirect |
| 32. #88058 | C22 | semidirect |
| 33. #88057 | C22 | semidirect |
| 34. #88056 | C22 | semidirect |
| 56. C2×C8×C13 | D4 | semidirect |
| 102. C2×#131 | D13 | semidirect |
| 133. C2×M16 | C2×D13 | semidirect |
| 135. C22×C8 | C2×D13 | semidirect |
| 178. C2×C8 | C22⋊D13 | semidirect |
| 191. C13 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#131 | 2 |
| #11719535 | 2 |
| #11719530 | 2 |
| C22×#6095 | 2 |
| #11718795 | 2 |
| #11718792 | 2 |
| #11718781 | 2 |
| #11718775 | 2 |
| #11718767 | 2 |
| #3057 | 13 |