Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 31. C13×Q16 | Q8 | semidirect |
| 107. Q16 | Dic26 | semidirect |
| 124. C13 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719275 | 2 |
| C4×C13×Q16 | 2 |
| Q16×Dic13 | 2 |
| #11718681 | 2 |
| #11718539 | 2 |
| #11718457 | 2 |
| #11718343 | 2 |
| C8×Dic26 | 2 |
| #3383 | 13 |