Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22576155 | C2 | semidirect |
| 2. #22576151 | C2 | semidirect |
| 3. #22576151 | C2 | semidirect |
| 5. #22576136 | C2 | semidirect |
| 6. Q8×Dic271 | C2 | semidirect |
| 8. #22576118 | C2 | semidirect |
| 9. #22576116 | C2 | semidirect |
| 10. C2×C4⋊Dic271 | C2 | semidirect |
| 11. C22⋊Q8×C271 | C2 | semidirect |
| 72. C271 | #552 | semidirect |
| 79. C22⋊Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22576155 | 2 |
| #22576151 | 2 |
| #22576144 | 2 |
| #22576136 | 2 |
| Q8×Dic271 | 2 |
| C4×C22⋊D271 | 2 |
| #22576118 | 2 |
| #22576116 | 2 |
| C2×C4⋊Dic271 | 2 |
| C22⋊Q8×C271 | 2 |
| #552 | 271 |