Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
504 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #14545659 | C2 | semidirect |
| 2. #14544171 | C2 | semidirect |
| 3. C2×#11763660 | C2 | semidirect |
| 4. #14544059 | C2 | semidirect |
| 5. #14543667 | C2 | semidirect |
| 6. #14543621 | C2 | semidirect |
| 26. #11763142 | C4 | semidirect |
| 28. #11763128 | C4 | semidirect |
| 32. #11762943 | C4 | semidirect |
| 34. C17×#450 | C4 | semidirect |
| 250. #450 | #595 | semidirect |
| 333. C17 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545659 | 2 |
| #14544171 | 2 |
| C2×#11763660 | 2 |
| #14544059 | 2 |
| #14543667 | 2 |
| #14543621 | 2 |
| #14539552 | 2 |
| #9264 | 17 |