Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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×#540 | C2 | semidirect |
| 2. #11719240 | C2 | semidirect |
| 3. #11718733 | C2 | semidirect |
| 4. #11718727 | C2 | semidirect |
| 5. #11718700 | C2 | semidirect |
| 6. #11718699 | C2 | semidirect |
| 7. #11718676 | C2 | semidirect |
| 8. #11718670 | C2 | semidirect |
| 9. #11718660 | C2 | semidirect |
| 87. #540 | D13 | semidirect |
| 168. C13 | #3259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#540 | 2 |
| #11719240 | 2 |
| #11718733 | 2 |
| #11718727 | 2 |
| #11718700 | 2 |
| #11718699 | 2 |
| #11718676 | 2 |
| #11718670 | 2 |
| #11718660 | 2 |
| #3259 | 13 |