Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 12. C13×Q32 | C4 | semidirect |
| 13. #88069 | C4 | semidirect |
| 14. Dic104 | C4 | semidirect |
| 49. #261 | Q32 | direct (N × H) |
| 58. Q32 | #261 | direct (N × H) |
| 80. C13 | C4×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#261 | 2 |
| D13×Q32 | 2 |
| #11718280 | 2 |
| #11718221 | 2 |
| C16×#261 | 2 |
| C4×Q32 | 13 |