Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556 | C2 | semidirect |
| 3. #11718748 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. #11718710 | C2 | semidirect |
| 6. #11718705 | C2 | semidirect |
| 7. C4×#6106 | C2 | semidirect |
| 8. #11718681 | C2 | semidirect |
| 9. #11718673 | C2 | semidirect |
| 10. #11718664 | C2 | semidirect |
| 11. #11718656 | C2 | semidirect |
| 100. #1055 | #41 | semidirect |
| 101. #556 | D13 | semidirect |
| 196. C13 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#556 | 2 |
| #11719260 | 2 |
| #11718748 | 2 |
| #11718739 | 2 |
| #11718710 | 2 |
| #11718705 | 2 |
| C4×#6106 | 2 |
| #11718681 | 2 |
| #11718673 | 2 |
| #11718664 | 2 |
| #11718656 | 2 |
| #3353 | 13 |