Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
256 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 16. C4⋊#1055 | C4 | semidirect |
| 76. C4×C13 | #107 | semidirect |
| 120. C13 | #1947 | semidirect |
| 155. C4 | #88047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×C4⋊C4 | 2 |
| C2×#88047 | 2 |
| #11718596 | 2 |
| C2×C4⋊#1055 | 2 |
| #11718121 | 2 |
| #1947 | 13 |