Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 42. C13×Q16 | Q8 | semidirect |
| 144. Q16 | Dic26 | semidirect |
| 169. C13 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719274 | 2 |
| C4×C13×Q16 | 2 |
| Q16×Dic13 | 2 |
| #11718683 | 2 |
| #11718539 | 2 |
| #11718535 | 2 |
| #11718460 | 2 |
| #11718452 | 2 |
| #11718344 | 2 |
| C8×Dic26 | 2 |
| #3383 | 13 |