Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
558 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14545513 | C2 | semidirect |
| 2. #14544916 | C2 | semidirect |
| 3. #14544292 | C2 | semidirect |
| 4. #14544213 | C2 | semidirect |
| 5. #14543638 | C2 | semidirect |
| 6. #14543609 | C2 | semidirect |
| 22. #11763185 | C4 | semidirect |
| 23. #11763156 | C4 | semidirect |
| 24. #11763155 | C4 | semidirect |
| 28. C17×#493 | C4 | semidirect |
| 117. #63242 | D8 | semidirect |
| 220. #493 | #595 | semidirect |
| 290. C17 | #9293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545513 | 2 |
| #14544916 | 2 |
| #14544292 | 2 |
| #14544213 | 2 |
| #14543638 | 2 |
| #14543609 | 2 |
| #14539698 | 2 |
| #9293 | 17 |