Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#16864643 | C2 | semidirect |
| 2. C2×#16864642 | C2 | semidirect |
| 3. C2×#16864641 | C2 | semidirect |
| 4. #22576158 | C2 | semidirect |
| 6. C8×Dic271 | C2 | semidirect |
| 7. C2×SD16×C271 | C2 | semidirect |
| 29. C271⋊C8 | D4 | semidirect |
| 37. C8×C271 | D4 | semidirect |
| 47. Dic271 | SD16 | semidirect |
| 52. C271 | #492 | semidirect |
| 57. C2×SD16 | D271 | semidirect |
| 90. C8 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864643 | 2 |
| C2×#16864642 | 2 |
| C2×#16864641 | 2 |
| #22576158 | 2 |
| #22576156 | 2 |
| C8×Dic271 | 2 |
| C2×SD16×C271 | 2 |
| #492 | 271 |