Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
530 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 530 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. #14544918 | C2 | semidirect |
| 2. #14544917 | C2 | semidirect |
| 3. C4×#10587532 | C2 | semidirect |
| 4. #14544340 | C2 | semidirect |
| 5. #14544131 | C2 | semidirect |
| 6. #14544130 | C2 | semidirect |
| 20. #11763212 | C4 | semidirect |
| 21. #11763185 | C4 | semidirect |
| 22. #11763156 | C4 | semidirect |
| 26. C17×#486 | C4 | semidirect |
| 150. #3622 | #104 | semidirect |
| 183. #486 | #595 | semidirect |
| 243. C17 | #9849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544918 | 2 |
| #14544917 | 2 |
| C4×#10587532 | 2 |
| #14544340 | 2 |
| #14544131 | 2 |
| #14544130 | 2 |
| #14539362 | 2 |
| #9849 | 17 |