Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
464 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #14544218 | C2 | semidirect |
| 4. #14544094 | C2 | semidirect |
| 5. #14543674 | C2 | semidirect |
| 6. #14543639 | C2 | semidirect |
| 26. #11763100 | C4 | semidirect |
| 27. #11763099 | C4 | semidirect |
| 28. #11763086 | C4 | semidirect |
| 32. C17×#474 | C4 | semidirect |
| 221. #474 | #595 | semidirect |
| 295. C17 | #9307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545647 | 2 |
| #14544654 | 2 |
| #14544218 | 2 |
| #14544094 | 2 |
| #14543674 | 2 |
| #14543639 | 2 |
| #14538576 | 2 |
| #9307 | 17 |