Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #14530581 | C2 | semidirect |
| 3. #14527546 | C2 | semidirect |
| 4. #14526746 | C2 | semidirect |
| 5. #14526745 | C2 | semidirect |
| 6. #14526744 | C2 | semidirect |
| 7. C17×#1331 | C2 | semidirect |
| 21. C4×#63214 | C22 | semidirect |
| 22. #11762562 | C22 | semidirect |
| 25. C4×C16×C17 | C22 | semidirect |
| 26. C17×#335 | C22 | semidirect |
| 150. #1331 | D17 | semidirect |
| 187. C4×C16 | C2×D17 | semidirect |
| 189. #335 | C2×D17 | semidirect |
| 232. C17 | #11661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D17 | 2 |
| #14530581 | 2 |
| #14527546 | 2 |
| #14526746 | 2 |
| #14526745 | 2 |
| #14526744 | 2 |
| C17×#1331 | 2 |
| #11661 | 17 |