Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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. C13×#384 | C2 | semidirect |
| 3. C2×#88049 | C2 | semidirect |
| 4. C2×C4×#1055 | C2 | semidirect |
| 12. #88128 | C4 | semidirect |
| 32. C2×#1055 | D4 | semidirect |
| 56. #384 | D13 | semidirect |
| 68. C4×C13 | #102 | semidirect |
| 105. C13 | #1957 | semidirect |
| 136. C4 | #88049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88128 | 2 |
| C13×#384 | 2 |
| C2×#88049 | 2 |
| C2×C4×#1055 | 2 |
| #1957 | 13 |