Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. C22×C13×C16 | C2 | semidirect |
| 3. C2×#88059 | C2 | semidirect |
| 4. #11718102 | C2 | direct (N × H) |
| 17. C2×C13×C16 | C22 | semidirect |
| 19. #88059 | C22 | semidirect |
| 69. C22×C16 | D13 | semidirect |
| 95. C2×C16 | C2×D13 | semidirect |
| 100. C2×C13 | #359 | semidirect |
| 128. C13 | C2×#359 | semidirect |
| 165. C2 | #11718102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| C22×C13×C16 | 2 |
| C2×#88059 | 2 |
| #11718102 | 2 |
| C2×#359 | 13 |