Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
574 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 84 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. #14545224 | C2 | semidirect |
| 4. #14544127 | C2 | semidirect |
| 5. #14543671 | C2 | semidirect |
| 6. #14543636 | C2 | semidirect |
| 25. #11763105 | C4 | semidirect |
| 26. #11763104 | C4 | semidirect |
| 27. #11763006 | C4 | semidirect |
| 32. C17×#460 | C4 | semidirect |
| 153. Q8×C17 | #104 | semidirect |
| 183. Dic34 | #104 | semidirect |
| 225. #460 | #595 | semidirect |
| 300. C17 | #9326 | semidirect |
| 364. Q8 | #10587548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545224 | 2 |
| #14544948 | 2 |
| #14544173 | 2 |
| #14544127 | 2 |
| #14543671 | 2 |
| #14543636 | 2 |
| #14538905 | 2 |
| #9326 | 17 |