Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C4×C13×M16 | C2 | semidirect |
| 3. C2×#88063 | C2 | semidirect |
| 4. #11718585 | C2 | semidirect |
| 28. C13×M16 | D4 | semidirect |
| 57. C4×M16 | D13 | semidirect |
| 65. C4×C13 | #100 | semidirect |
| 97. M16 | D52 | semidirect |
| 103. C13 | #1965 | semidirect |
| 129. C4 | #88063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88128 | 2 |
| C4×C13×M16 | 2 |
| C2×#88063 | 2 |
| #11718585 | 2 |
| #1965 | 13 |