Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 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. #14529532 | C2 | semidirect |
| 5. #14526880 | C2 | semidirect |
| 6. #14526878 | C2 | semidirect |
| 7. C2×C4×C16×C17 | C2 | semidirect |
| 16. #11762614 | C4 | semidirect |
| 17. #11762611 | C4 | semidirect |
| 122. C2×C4×C16 | D17 | semidirect |
| 191. C17 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762617 | 2 |
| #14530492 | 2 |
| #14529672 | 2 |
| #14529532 | 2 |
| #14526880 | 2 |
| #14526878 | 2 |
| C2×C4×C16×C17 | 2 |
| #13151 | 17 |