Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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. C13×#529 | C2 | semidirect |
| 2. #11719182 | C2 | semidirect |
| 3. #11718728 | C2 | semidirect |
| 4. #11718726 | C2 | semidirect |
| 5. #11718719 | C2 | semidirect |
| 6. #11718716 | C2 | semidirect |
| 7. #11718709 | C2 | semidirect |
| 8. #11718699 | C2 | semidirect |
| 9. #11718687 | C2 | semidirect |
| 10. #11718675 | C2 | semidirect |
| 11. C2×#88043 | C2 | semidirect |
| 111. #1055 | #41 | semidirect |
| 113. #529 | D13 | semidirect |
| 219. C13 | #3180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| #11719182 | 2 |
| #11718728 | 2 |
| #11718726 | 2 |
| #11718719 | 2 |
| #11718716 | 2 |
| #11718709 | 2 |
| #11718699 | 2 |
| #11718687 | 2 |
| #11718675 | 2 |
| C2×#88043 | 2 |
| #3180 | 13 |