Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 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. C2×Q8×Dic13 | C2 | semidirect |
| 3. C13×#448 | C2 | semidirect |
| 4. #11718888 | C2 | semidirect |
| 5. #11718825 | C2 | semidirect |
| 6. #11718824 | C2 | semidirect |
| 7. #11718694 | C2 | semidirect |
| 8. #11718478 | C2 | semidirect |
| 9. #11718455 | C2 | semidirect |
| 10. #11718397 | C2 | semidirect |
| 11. #11718380 | C2 | semidirect |
| 88. Q8×C13 | #41 | semidirect |
| 122. #448 | D13 | semidirect |
| 222. C13 | #3112 | semidirect |
| 229. Q8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic13 | 2 |
| #11719301 | 2 |
| C13×#448 | 2 |
| #11718888 | 2 |
| #11718825 | 2 |
| #11718824 | 2 |
| #11718694 | 2 |
| #11718478 | 2 |
| #11718455 | 2 |
| #11718397 | 2 |
| #11718380 | 2 |
| #3112 | 13 |