Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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×#88118 | C2 | semidirect |
| 3. C42×#261 | C2 | semidirect |
| 4. #11719052 | C2 | semidirect |
| 9. C13×C4⋊Q8 | C4 | semidirect |
| 10. #88201 | C4 | semidirect |
| 13. #88128 | C4 | semidirect |
| 30. C4×#261 | D4 | semidirect |
| 68. C4×C13 | #104 | semidirect |
| 75. C4⋊Q8 | #261 | semidirect |
| 109. C13 | #1962 | semidirect |
| 139. C4 | #88118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719430 | 2 |
| C2×#88118 | 2 |
| C42×#261 | 2 |
| #11719052 | 2 |
| #1962 | 13 |