Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 512 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. D17⋊#443 | C2 | semidirect |
| 2. D17⋊#361 | C2 | semidirect |
| 3. #14545092 | C2 | semidirect |
| 4. #14544931 | C2 | semidirect |
| 5. #14543859 | C2 | semidirect |
| 6. #14543827 | C2 | semidirect |
| 24. #11763247 | C4 | semidirect |
| 26. #11763245 | C4 | semidirect |
| 27. #11763244 | C4 | semidirect |
| 32. C17×#509 | C4 | semidirect |
| 124. Q16×C17 | C22⋊C4 | semidirect |
| 128. D8×C17 | C22⋊C4 | semidirect |
| 137. Dic68 | C22⋊C4 | semidirect |
| 140. D136 | C22⋊C4 | semidirect |
| 236. #509 | #595 | semidirect |
| 316. C17 | #13029 | semidirect |
| 340. Q16 | C22⋊#595 | semidirect |
| 353. D8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#443 | 2 |
| D17⋊#361 | 2 |
| #14545092 | 2 |
| #14544931 | 2 |
| #14543859 | 2 |
| #14543827 | 2 |
| D17×#509 | 2 |
| #13029 | 17 |