Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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. #14545131 | C2 | semidirect |
| 2. C2×#11763734 | C2 | semidirect |
| 5. #14543862 | C2 | semidirect |
| 6. #14543856 | C2 | semidirect |
| 22. #11763227 | C4 | semidirect |
| 23. #11763226 | C4 | semidirect |
| 25. #11763225 | C4 | semidirect |
| 30. C17×#504 | C4 | semidirect |
| 186. #504 | #595 | semidirect |
| 254. C17 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545131 | 2 |
| C2×#11763734 | 2 |
| #14544672 | 2 |
| #14544670 | 2 |
| #14543862 | 2 |
| #14543856 | 2 |
| #14541885 | 2 |
| #12833 | 17 |