Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22576149 | C2 | semidirect |
| 4. #22576144 | C2 | semidirect |
| 6. Q8×Dic271 | C2 | semidirect |
| 7. #22576122 | C2 | semidirect |
| 8. (C22⋊D271)⋊C4 | C2 | semidirect |
| 9. #22576118 | C2 | semidirect |
| 10. C2×C4×Dic271 | C2 | semidirect |
| 11. C22⋊Q8×C271 | C2 | semidirect |
| 74. C271 | #529 | semidirect |
| 80. 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 |
| #22576149 | 2 |
| #22576144 | 2 |
| #22576134 | 2 |
| Q8×Dic271 | 2 |
| #22576122 | 2 |
| (C22⋊D271)⋊C4 | 2 |
| #22576118 | 2 |
| C2×C4×Dic271 | 2 |
| C22⋊Q8×C271 | 2 |
| #529 | 271 |