Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
564 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14545316 | C2 | semidirect |
| 3. #14544222 | C2 | semidirect |
| 5. #14543659 | C2 | semidirect |
| 6. #14543625 | C2 | semidirect |
| 26. #11763140 | C4 | semidirect |
| 27. #11763137 | C4 | semidirect |
| 31. #11762960 | C4 | semidirect |
| 34. C17×#450 | C4 | semidirect |
| 129. C22⋊#595 | SD16 | semidirect |
| 275. #450 | #595 | semidirect |
| 359. C17 | #9278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545316 | 2 |
| #14544923 | 2 |
| #14544222 | 2 |
| C2×#11763660 | 2 |
| #14543659 | 2 |
| #14543625 | 2 |
| #14539538 | 2 |
| #9278 | 17 |