Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719402 | C2 | semidirect |
| 3. C13×#499 | C2 | semidirect |
| 4. #11718730 | C2 | semidirect |
| 5. #11718728 | C2 | semidirect |
| 6. #11718550 | C2 | semidirect |
| 7. #11718547 | C2 | semidirect |
| 8. #11718525 | C2 | semidirect |
| 9. #11718513 | C2 | semidirect |
| 10. #11718354 | C2 | semidirect |
| 11. #11718350 | C2 | semidirect |
| 93. #499 | D13 | semidirect |
| 176. C13 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719403 | 2 |
| #11719402 | 2 |
| C13×#499 | 2 |
| #11718730 | 2 |
| #11718728 | 2 |
| #11718550 | 2 |
| #11718547 | 2 |
| #11718525 | 2 |
| #11718513 | 2 |
| #11718354 | 2 |
| #11718350 | 2 |
| #3174 | 13 |