Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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 | semidirect |
| 9. #88237 | C4 | semidirect |
| 13. D13⋊M16 | C4 | semidirect |
| 16. C2×C13×C4⋊C4 | C4 | semidirect |
| 18. C2×C4⋊Dic13 | C4 | semidirect |
| 22. #88146 | C4 | semidirect |
| 43. C4×#261 | C2×C4 | semidirect |
| 45. #6118 | C2×C4 | semidirect |
| 129. C2×C4⋊C4 | #261 | semidirect |
| 172. C13 | #1733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88237 | 2 |
| C2×D13⋊M16 | 2 |
| C2×#88146 | 2 |
| #11718247 | 2 |
| #1733 | 13 |