Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 39 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×#16864644 | C2 | semidirect |
| 5. #22576091 | C2 | semidirect |
| 6. #22576085 | C2 | semidirect |
| 7. #103×C271 | C2 | semidirect |
| 51. C271 | #470 | semidirect |
| 59. #103 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864644 | 2 |
| C2×#16864637 | 2 |
| #22576140 | 2 |
| #22576136 | 2 |
| #22576091 | 2 |
| #22576085 | 2 |
| #103×C271 | 2 |
| #470 | 271 |