Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
466 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 82 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. D17⋊#444 | C2 | semidirect |
| 2. #14545112 | C2 | semidirect |
| 3. #14545100 | C2 | semidirect |
| 4. #14544938 | C2 | semidirect |
| 5. #14543862 | C2 | semidirect |
| 6. #14543830 | C2 | semidirect |
| 25. #11763250 | C4 | semidirect |
| 26. #11763247 | C4 | semidirect |
| 28. #11763244 | C4 | semidirect |
| 32. C17×#510 | C4 | semidirect |
| 218. #510 | #595 | semidirect |
| 298. C17 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#444 | 2 |
| #14545112 | 2 |
| #14545100 | 2 |
| #14544938 | 2 |
| #14543862 | 2 |
| #14543830 | 2 |
| #14541919 | 2 |
| #13024 | 17 |