Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 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. #14531509 | C2 | semidirect |
| 3. #14529608 | C2 | semidirect |
| 4. #14529131 | C2 | semidirect |
| 5. #14528915 | C2 | semidirect |
| 6. C17×#1746 | C2 | semidirect |
| 10. #11763186 | C4 | semidirect |
| 31. C2×D136 | C2×C4 | semidirect |
| 33. #10587560 | C2×C4 | semidirect |
| 36. C4×C8×C17 | C2×C4 | semidirect |
| 91. #1746 | D17 | semidirect |
| 139. C4×C8 | C4×D17 | semidirect |
| 142. C17 | #22276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763186 | 2 |
| #14531509 | 2 |
| #14529608 | 2 |
| #14529131 | 2 |
| #14528915 | 2 |
| C17×#1746 | 2 |
| #22276 | 17 |