Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 4. #11718105 | C2 | direct (N × H) |
| 8. C13×M32 | C4 | semidirect |
| 10. C2×C13×C16 | C4 | semidirect |
| 28. C13×C16 | C2×C4 | semidirect |
| 60. M32 | Dic13 | semidirect |
| 62. C2×C16 | Dic13 | semidirect |
| 69. C2×C13 | #365 | semidirect |
| 84. C16 | C2×Dic13 | semidirect |
| 85. C13 | C2×#365 | semidirect |
| 111. C2 | #11718105 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×M32 | 2 |
| C2×#88059 | 2 |
| C2×#88057 | 2 |
| #11718105 | 2 |
| C2×#365 | 13 |