Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 76 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. #14545676 | C2 | semidirect |
| 2. #14544175 | C2 | semidirect |
| 3. #14544173 | C2 | semidirect |
| 4. #14544144 | C2 | semidirect |
| 5. #14543641 | C2 | semidirect |
| 6. #14543607 | C2 | semidirect |
| 22. #11763185 | C4 | semidirect |
| 23. #11763182 | C4 | semidirect |
| 24. #11763161 | C4 | semidirect |
| 28. C17×#486 | C4 | semidirect |
| 185. #486 | #595 | semidirect |
| 249. C17 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545676 | 2 |
| #14544175 | 2 |
| #14544173 | 2 |
| #14544144 | 2 |
| #14543641 | 2 |
| #14543607 | 2 |
| #14539718 | 2 |
| #9281 | 17 |