Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
236 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 2. C2×C13×M32 | C2 | semidirect |
| 3. C2×#88052 | C2 | semidirect |
| 4. #11718106 | C2 | direct (N × H) |
| 15. C13×M32 | C22 | semidirect |
| 18. #88052 | C22 | semidirect |
| 70. C2×M32 | D13 | semidirect |
| 97. M32 | C2×D13 | semidirect |
| 102. C2×C13 | #349 | semidirect |
| 129. C13 | C2×#349 | semidirect |
| 169. C2 | #11718106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6094 | 2 |
| C2×C13×M32 | 2 |
| C2×#88052 | 2 |
| #11718106 | 2 |
| C2×#349 | 13 |