Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×#88124 | C2 | semidirect |
| 3. C13×#431 | C2 | semidirect |
| 4. #11718508 | C2 | semidirect |
| 5. #11718490 | C2 | semidirect |
| 8. #11718383 | C2 | semidirect |
| 9. #11718382 | C2 | semidirect |
| 10. #11718358 | C2 | semidirect |
| 11. #11718344 | C2 | semidirect |
| 113. #431 | D13 | semidirect |
| 203. C13 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| C2×#88124 | 2 |
| C13×#431 | 2 |
| #11718508 | 2 |
| #11718490 | 2 |
| #11718397 | 2 |
| #11718396 | 2 |
| #11718383 | 2 |
| #11718382 | 2 |
| #11718358 | 2 |
| #11718344 | 2 |
| #3232 | 13 |