Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 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×#88074 | C2 | semidirect |
| 3. C2×#88073 | C2 | semidirect |
| 4. #11718128 | C2 | direct (N × H) |
| 5. C25×C13 | C4 | semidirect |
| 10. C13×#120 | C4 | semidirect |
| 13. C2×C13×C22⋊C4 | C4 | semidirect |
| 17. #88074 | C22 | semidirect |
| 19. #88073 | C22 | semidirect |
| 26. C24×C13 | C2×C4 | semidirect |
| 43. C13×C22⋊C4 | C2×C4 | semidirect |
| 120. C25 | Dic13 | semidirect |
| 126. #120 | Dic13 | semidirect |
| 130. C2×C22⋊C4 | Dic13 | semidirect |
| 142. C2×C13 | AΣL(1,𝔽16) | semidirect |
| 150. C24 | C2×Dic13 | semidirect |
| 172. C22⋊C4 | C2×Dic13 | semidirect |
| 173. C13 | C2×AΣL(1,𝔽16) | semidirect |
| 247. C2 | #11718128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#120 | 2 |
| C2×#88074 | 2 |
| C2×#88073 | 2 |
| #11718128 | 2 |
| C2×AΣL(1,𝔽16) | 13 |