Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 1. C13×#536 | C2 | semidirect |
| 2. #11719240 | C2 | semidirect |
| 3. #11718899 | C2 | semidirect |
| 4. #11718888 | C2 | semidirect |
| 5. #11718746 | C2 | semidirect |
| 6. #11718744 | C2 | semidirect |
| 7. #11718743 | C2 | semidirect |
| 8. #11718719 | C2 | semidirect |
| 9. #11718718 | C2 | semidirect |
| 10. #11718717 | C2 | semidirect |
| 11. #11718661 | C2 | semidirect |
| 101. #536 | D13 | semidirect |
| 192. C13 | #3221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#536 | 2 |
| #11719240 | 2 |
| #11718899 | 2 |
| #11718888 | 2 |
| #11718746 | 2 |
| #11718744 | 2 |
| #11718743 | 2 |
| #11718719 | 2 |
| #11718718 | 2 |
| #11718717 | 2 |
| #11718661 | 2 |
| #3221 | 13 |