Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 1. C2×C13×H(5,𝔽2) | C2 | semidirect |
| 2. #11719509 | C2 | semidirect |
| 3. #11718905 | C2 | semidirect |
| 4. #11718904 | C2 | semidirect |
| 5. C2×#88074 | C2 | semidirect |
| 11. C22×C22⋊D13 | C22 | semidirect |
| 13. C2×C22⋊Dic13 | C22 | semidirect |
| 15. #88191 | C22 | semidirect |
| 16. #88189 | C22 | semidirect |
| 18. #88074 | C22 | semidirect |
| 20. C24×C13 | D4 | semidirect |
| 22. C23×D13 | C23 | semidirect |
| 31. C2×D4×C13 | D4 | semidirect |
| 34. C22×C4×C13 | D4 | semidirect |
| 39. C22×Dic13 | C23 | semidirect |
| 42. C22⋊Dic13 | C23 | semidirect |
| 72. C2×H(5,𝔽2) | D13 | semidirect |
| 114. C24 | C22⋊D13 | semidirect |
| 127. C2×D4 | C22⋊D13 | semidirect |
| 132. C22×C4 | C22⋊D13 | semidirect |
| 138. C13 | #3026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(5,𝔽2) | 2 |
| #11719509 | 2 |
| #11718905 | 2 |
| #11718904 | 2 |
| C2×#88074 | 2 |
| #3026 | 13 |