Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
168 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11718217 | C2 | direct (N × H) |
| 8. C2×#6092 | C4 | semidirect |
| 11. #88098 | C4 | semidirect |
| 13. C2×C13×C16 | C4 | semidirect |
| 14. C2×#6090 | C4 | semidirect |
| 15. #88038 | C4 | semidirect |
| 30. #6092 | C2×C4 | semidirect |
| 31. C13×C16 | C2×C4 | semidirect |
| 32. #6090 | C2×C4 | semidirect |
| 70. C2×C16 | #261 | semidirect |
| 73. C2×C13 | #347 | semidirect |
| 92. C16 | C2×#261 | semidirect |
| 93. C13 | C2×#347 | semidirect |
| 119. C2 | #11718217 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88100 | 2 |
| C2×#88098 | 2 |
| C2×#88038 | 2 |
| #11718217 | 2 |
| C2×#347 | 13 |