Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
510 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 102 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. #14544523 | C2 | semidirect |
| 3. #14544522 | C2 | semidirect |
| 5. #14543667 | C2 | semidirect |
| 6. #14543665 | C2 | semidirect |
| 8. C2×#10587678 | C4 | semidirect |
| 14. #11763816 | C4 | semidirect |
| 15. #11763783 | C4 | semidirect |
| 18. #11763774 | C4 | semidirect |
| 24. #11763662 | C4 | semidirect |
| 25. #11763660 | C4 | semidirect |
| 29. #11762547 | C4 | semidirect |
| 30. #11762545 | C4 | semidirect |
| 31. #11762543 | C4 | semidirect |
| 32. C17×#327 | C4 | semidirect |
| 249. #327 | #595 | semidirect |
| 305. C17 | #8239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545498 | 2 |
| #14544523 | 2 |
| #14544522 | 2 |
| #14544160 | 2 |
| #14543667 | 2 |
| #14543665 | 2 |
| #14527272 | 2 |
| #8239 | 17 |