Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. C2×#88104 | C2 | semidirect |
| 4. #11719079 | C2 | semidirect |
| 6. (C2×#261)⋊C8 | C2 | semidirect |
| 7. #11718247 | C2 | semidirect |
| 23. C13×#103 | C4 | semidirect |
| 24. #88075 | C4 | semidirect |
| 25. #88061 | C4 | semidirect |
| 26. #88049 | C4 | semidirect |
| 127. #103 | #261 | semidirect |
| 168. C13 | #1866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88240 | 2 |
| C2×#88118 | 2 |
| C2×#88104 | 2 |
| #11719079 | 2 |
| #11718465 | 2 |
| (C2×#261)⋊C8 | 2 |
| #11718247 | 2 |
| #1866 | 13 |