Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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×#117 | C2 | semidirect |
| 3. C2×C22⋊#1055 | C2 | semidirect |
| 4. #11718664 | C2 | direct (N × H) |
| 5. C2×#88049 | C2 | semidirect |
| 6. C2×#88049 | C2 | semidirect |
| 7. C2×#88048 | C2 | semidirect |
| 8. C2×#88047 | C2 | semidirect |
| 13. C13×#117 | C22 | semidirect |
| 24. C22⋊#1055 | C22 | semidirect |
| 25. #88049 | C22 | semidirect |
| 26. #88049 | C22 | semidirect |
| 27. #88048 | C22 | semidirect |
| 28. #88047 | C22 | semidirect |
| 91. C2×#117 | D13 | semidirect |
| 125. #117 | C2×D13 | semidirect |
| 138. C2×C13 | #482 | semidirect |
| 173. C13 | C2×#482 | semidirect |
| 225. C2 | #11718664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#117 | 2 |
| C2×#88184 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718664 | 2 |
| C2×#88049 | 2 |
| C2×#88048 | 2 |
| C2×#88047 | 2 |
| C2×#482 | 13 |