Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 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. #11718740 | C2 | semidirect |
| 5. #11718709 | C2 | semidirect |
| 6. #11718706 | C2 | semidirect |
| 7. C4×#6106 | C2 | semidirect |
| 8. #11718682 | C2 | semidirect |
| 9. D4×#1055 | C2 | semidirect |
| 10. #11718664 | C2 | semidirect |
| 11. #11718659 | C2 | semidirect |
| 99. #556 | D13 | semidirect |
| 193. C13 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#556 | 2 |
| #11719268 | 2 |
| #11718748 | 2 |
| #11718740 | 2 |
| #11718709 | 2 |
| #11718706 | 2 |
| C4×#6106 | 2 |
| #11718682 | 2 |
| D4×#1055 | 2 |
| #11718664 | 2 |
| #11718659 | 2 |
| #3340 | 13 |