Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545749 | C2 | semidirect |
| 2. #14545106 | C2 | semidirect |
| 3. C2×#11763724 | C2 | semidirect |
| 4. #14544671 | C2 | semidirect |
| 5. #14543863 | C2 | semidirect |
| 6. #14543847 | C2 | semidirect |
| 25. #11763081 | C4 | semidirect |
| 26. #11763080 | C4 | semidirect |
| 27. #11763079 | C4 | semidirect |
| 32. C17×#473 | C4 | semidirect |
| 230. #473 | #595 | semidirect |
| 305. C17 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545749 | 2 |
| #14545106 | 2 |
| C2×#11763724 | 2 |
| #14544671 | 2 |
| #14543863 | 2 |
| #14543847 | 2 |
| #14538506 | 2 |
| #13071 | 17 |