Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
156 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. #11718222 | C2 | semidirect |
| 5. #11718221 | C2 | semidirect |
| 14. C13×M32 | C4 | semidirect |
| 15. #88052 | C4 | semidirect |
| 16. #88038 | C4 | semidirect |
| 32. C13×C16 | C2×C4 | semidirect |
| 33. #6090 | C2×C4 | semidirect |
| 72. M32 | #261 | semidirect |
| 99. C16 | C2×#261 | semidirect |
| 100. C13 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719092 | 2 |
| C2×#88102 | 2 |
| D13×M32 | 2 |
| #11718222 | 2 |
| #11718221 | 2 |
| #2159 | 13 |