Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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×#559 | C2 | semidirect |
| 2. #11719289 | C2 | semidirect |
| 3. #11718737 | C2 | semidirect |
| 5. #11718720 | C2 | semidirect |
| 6. #11718715 | C2 | semidirect |
| 7. #11718692 | C2 | semidirect |
| 8. C4×#6106 | C2 | semidirect |
| 9. Q8×#1055 | C2 | semidirect |
| 10. C4×#6105 | C2 | semidirect |
| 11. #11718677 | C2 | semidirect |
| 104. #559 | D13 | semidirect |
| 201. C13 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#559 | 2 |
| #11719289 | 2 |
| #11718737 | 2 |
| #11718733 | 2 |
| #11718720 | 2 |
| #11718715 | 2 |
| #11718692 | 2 |
| C4×#6106 | 2 |
| Q8×#1055 | 2 |
| C4×#6105 | 2 |
| #11718677 | 2 |
| #3394 | 13 |