Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 146 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. #11718247 | C2 | direct (N × H) |
| 10. C2×C4×#261 | C4 | semidirect |
| 14. C2×#6118 | C4 | semidirect |
| 16. C2×C13×C4⋊C4 | C4 | semidirect |
| 18. C2×C4⋊Dic13 | C4 | semidirect |
| 22. #88146 | C4 | semidirect |
| 45. C4×#261 | C2×C4 | semidirect |
| 48. #6118 | C2×C4 | semidirect |
| 50. C13×C4⋊C4 | C2×C4 | semidirect |
| 54. C4⋊Dic13 | C2×C4 | semidirect |
| 130. C2×C4⋊C4 | #261 | semidirect |
| 137. C2×C13 | #339 | semidirect |
| 169. C4⋊C4 | C2×#261 | semidirect |
| 177. C13 | C2×#339 | semidirect |
| 237. C2 | #11718247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#261 | 2 |
| C22×#6118 | 2 |
| C2×#88146 | 2 |
| #11718247 | 2 |
| C2×#339 | 13 |