Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #11718120 | C2 | semidirect |
| 52. C2×C4×C13 | M16 | semidirect |
| 107. C13 | #1463 | semidirect |
| 126. C2×C4 | #6099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C4⋊C4 | 2 |
| #11718868 | 2 |
| #11718120 | 2 |
| #1463 | 13 |