Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #22576190 | C2 | semidirect |
| 2. C2×#16864642 | C2 | semidirect |
| 3. #22576167 | C2 | semidirect |
| 4. #22576095 | C2 | semidirect |
| 5. #22576078 | C2 | semidirect |
| 6. #22576077 | C2 | semidirect |
| 51. C271 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22576190 | 2 |
| C2×#16864642 | 2 |
| #22576167 | 2 |
| #22576095 | 2 |
| #22576078 | 2 |
| #22576077 | 2 |
| AGL(1,ℤ/8)×C271 | 2 |
| #471 | 271 |