Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14537352 | C2 | direct (N × H) |
| 3. C2×#11762836 | C2 | semidirect |
| 4. C2×#11762833 | C2 | semidirect |
| 5. C22×C4⋊#3622 | C2 | semidirect |
| 11. #11762836 | C22 | semidirect |
| 12. #11762833 | C22 | semidirect |
| 17. C2×C4⋊#3622 | C22 | semidirect |
| 114. C2×C4×C17 | #131 | semidirect |
| 147. C4×C17 | C2×#131 | semidirect |
| 171. C2×C17 | #2906 | semidirect |
| 210. C17 | C2×#2906 | semidirect |
| 262. C2×C4 | #10587634 | semidirect |
| 289. C4 | C2×#10587634 | semidirect |
| 293. C2 | #14537352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587634 | 2 |
| #14537352 | 2 |
| C2×#11762836 | 2 |
| C2×#11762833 | 2 |
| C22×C4⋊#3622 | 2 |
| C2×C4×#41×C17 | 2 |
| C2×#2906 | 17 |