Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 74. C2×C4×C13 | Q16 | semidirect |
| 173. C13 | #2056 | semidirect |
| 200. C2×C4 | #6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6107 | 2 |
| C13×#391 | 2 |
| C2×#88075 | 2 |
| C2×#88050 | 2 |
| #11718590 | 2 |
| C2×C4⋊#1055 | 2 |
| #11718121 | 2 |
| #2056 | 13 |