Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. #11719270 | C2 | semidirect |
| 2. C13×#436 | C2 | semidirect |
| 3. #11718796 | C2 | semidirect |
| 4. #11718782 | C2 | semidirect |
| 5. #11718508 | C2 | semidirect |
| 6. #11718398 | C2 | semidirect |
| 7. #11718397 | C2 | semidirect |
| 8. C4×D104 | C2 | semidirect |
| 9. #11718344 | C2 | semidirect |
| 90. #436 | D13 | semidirect |
| 163. C13 | #3355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719270 | 2 |
| C13×#436 | 2 |
| #11718796 | 2 |
| #11718782 | 2 |
| #11718508 | 2 |
| #11718398 | 2 |
| #11718397 | 2 |
| C4×D104 | 2 |
| #11718344 | 2 |
| #3355 | 13 |