Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#88056 | C2 | semidirect |
| 5. C2×#88050 | C2 | semidirect |
| 6. C13×#340 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 20. #88151 | C4 | semidirect |
| 47. C2×Dic26 | C2×C4 | semidirect |
| 53. C13×C4⋊C4 | C2×C4 | semidirect |
| 110. #340 | D13 | semidirect |
| 124. C2×D13 | #103 | semidirect |
| 194. C4⋊C4 | C4×D13 | semidirect |
| 197. C13 | #1872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88151 | 2 |
| C2×C4⋊C4×D13 | 2 |
| C2×#88060 | 2 |
| C2×#88056 | 2 |
| C2×#88050 | 2 |
| C13×#340 | 2 |
| #11718121 | 2 |
| #1872 | 13 |