Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
464 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 3. #14544737 | C2 | semidirect |
| 4. #14544730 | C2 | semidirect |
| 5. #14543665 | C2 | semidirect |
| 6. #14543625 | C2 | semidirect |
| 27. #11762547 | C4 | semidirect |
| 28. #11762545 | C4 | semidirect |
| 29. #11762543 | C4 | semidirect |
| 30. C17×#327 | C4 | semidirect |
| 239. #327 | #595 | semidirect |
| 293. C17 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545651 | 2 |
| #14544767 | 2 |
| #14544737 | 2 |
| #14544730 | 2 |
| #14543665 | 2 |
| #14543625 | 2 |
| #14527272 | 2 |
| #8875 | 17 |