Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
370 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 17. #11762560 | C4 | semidirect |
| 18. #11762559 | C4 | semidirect |
| 19. C17×#334 | C4 | semidirect |
| 107. C8×C17 | #106 | semidirect |
| 110. #3622 | #106 | semidirect |
| 147. #334 | #595 | semidirect |
| 180. C17 | #9621 | semidirect |
| 245. C8 | #10587533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544896 | 2 |
| #14544720 | 2 |
| #14544578 | 2 |
| #14543663 | 2 |
| D17×#334 | 2 |
| #9621 | 17 |