Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
720 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×#10587539 | C2 | semidirect |
| 3. #14543878 | C2 | semidirect |
| 7. #11763714 | C4 | direct (N × H) |
| 11. C2×C4×D68 | C4 | semidirect |
| 14. #11762711 | C4 | semidirect |
| 16. #11762679 | C4 | semidirect |
| 17. C43×C17 | C4 | semidirect |
| 46. #10587539 | C2×C4 | semidirect |
| 65. C2×D68 | C42 | semidirect |
| 83. C42×C17 | C42 | semidirect |
| 160. C4×C17 | #353 | semidirect |
| 173. C43 | #595 | semidirect |
| 212. C17 | C4×#353 | semidirect |
| 256. C42 | C4×#595 | semidirect |
| 323. C4 | #11763714 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763714 | 2 |
| C4×#10587539 | 2 |
| #14543878 | 2 |
| C4×#10587560 | 2 |
| C4×#353 | 17 |