Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 2. C2×#88107 | C2 | semidirect |
| 3. #11718300 | C2 | semidirect |
| 4. #11718294 | C2 | semidirect |
| 5. C2×C13×#41 | C4 | semidirect |
| 8. #88201 | C4 | semidirect |
| 10. #88194 | C4 | semidirect |
| 14. #88180 | C4 | semidirect |
| 20. C2×Q8×C13 | C2×C4 | semidirect |
| 22. C2×D4×C13 | C2×C4 | semidirect |
| 37. C4×Dic13 | C2×C4 | semidirect |
| 38. C4×Dic13 | C2×C4 | semidirect |
| 85. C2×#41 | #261 | semidirect |
| 105. C2×Q8 | C2×#261 | semidirect |
| 113. C2×D4 | C2×#261 | semidirect |
| 125. C13 | #2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719535 | 2 |
| C2×#88107 | 2 |
| #11718300 | 2 |
| #11718294 | 2 |
| #2127 | 13 |