Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. #11718782 | C2 | semidirect |
| 5. #11718781 | C2 | semidirect |
| 6. #11718384 | C2 | semidirect |
| 7. #11718383 | C2 | semidirect |
| 8. #11718382 | C2 | semidirect |
| 29. #88058 | C22 | semidirect |
| 30. #88057 | C22 | semidirect |
| 31. #88056 | C22 | semidirect |
| 32. #88056 | C22 | semidirect |
| 180. C13 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88180 | 2 |
| C2×#88178 | 2 |
| C13×#407 | 2 |
| #11718782 | 2 |
| #11718781 | 2 |
| #11718384 | 2 |
| #11718383 | 2 |
| #11718382 | 2 |
| #3095 | 13 |