Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q32 | C2 | semidirect |
| 3. C2×#88069 | C2 | semidirect |
| 4. D13×Q32 | C2 | direct (N × H) |
| 5. C2×Dic104 | C2 | semidirect |
| 14. C13×Q32 | C22 | semidirect |
| 16. #88069 | C22 | semidirect |
| 18. Dic104 | C22 | semidirect |
| 59. C2×Q32 | D13 | direct (N × H) |
| 62. C2×D13 | Q32 | direct (N × H) |
| 78. Q32 | C2×D13 | direct (N × H) |
| 82. C2×C13 | C2×Q32 | semidirect |
| 84. D13 | C2×Q32 | direct (N × H) |
| 103. C13 | C22×Q32 | semidirect |
| 129. C2 | D13×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| C2×C13×Q32 | 2 |
| C2×#88069 | 2 |
| D13×Q32 | 2 |
| C2×Dic104 | 2 |
| C2×C16×D13 | 2 |
| C22×Q32 | 13 |