Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
316 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14545160 | C2 | semidirect |
| 2. #14544506 | C2 | semidirect |
| 3. #14543759 | C2 | semidirect |
| 4. #14543758 | C2 | semidirect |
| 5. #14543755 | C2 | semidirect |
| 6. #14543754 | C2 | semidirect |
| 17. #11763209 | C4 | semidirect |
| 18. #11763184 | C4 | semidirect |
| 23. #11762922 | C4 | semidirect |
| 26. C17×#442 | C4 | semidirect |
| 161. #442 | #595 | semidirect |
| 210. C17 | #11770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545160 | 2 |
| #14544506 | 2 |
| #14543759 | 2 |
| #14543758 | 2 |
| #14543755 | 2 |
| #14543754 | 2 |
| #14539432 | 2 |
| #11770 | 17 |