Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
172 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 22. C13×M16 | C8 | semidirect |
| 29. #6099 | C8 | semidirect |
| 87. M16 | #1057 | semidirect |
| 97. C13 | #1278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719119 | 2 |
| C2×C4×#1057 | 2 |
| M16×Dic13 | 2 |
| #1278 | 13 |