Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 13. C8×#3624 | C4 | semidirect |
| 14. C8×#3624 | C4 | semidirect |
| 17. #11762560 | C4 | semidirect |
| 18. #11762559 | C4 | semidirect |
| 19. C17×#334 | C4 | semidirect |
| 34. #10587533 | C8 | semidirect |
| 89. #3624 | #106 | semidirect |
| 92. C8×C17 | C4×C8 | semidirect |
| 95. #3622 | C4×C8 | semidirect |
| 125. #334 | #595 | semidirect |
| 155. C17 | C8×#106 | semidirect |
| 207. C8 | C8×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587533 | 2 |
| #14544577 | 2 |
| C8×#63242 | 2 |
| #14543618 | 2 |
| D17×#334 | 2 |
| C8×#106 | 17 |