Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 470 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. #14545478 | C2 | semidirect |
| 2. #14544689 | C2 | semidirect |
| 5. #14543684 | C2 | semidirect |
| 6. #14543666 | C2 | semidirect |
| 28. #11762849 | C4 | semidirect |
| 29. #11762815 | C4 | semidirect |
| 30. #11762813 | C4 | semidirect |
| 32. C17×#428 | C4 | semidirect |
| 232. #428 | #595 | semidirect |
| 303. C17 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545478 | 2 |
| #14544689 | 2 |
| #14544221 | 2 |
| #14544061 | 2 |
| #14543684 | 2 |
| #14543666 | 2 |
| #14538726 | 2 |
| #9348 | 17 |