Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D271 | C2 | semidirect |
| 3. #22576159 | C2 | semidirect |
| 4. #22576146 | C2 | semidirect |
| 5. #22576145 | C2 | semidirect |
| 6. #22576142 | C2 | semidirect |
| 7. #22576140 | C2 | semidirect |
| 8. #22576139 | C2 | semidirect |
| 9. #22576136 | C2 | semidirect |
| 10. #22576118 | C2 | semidirect |
| 11. C22⋊Q8×C271 | C2 | semidirect |
| 83. C271 | #536 | semidirect |
| 94. C22⋊Q8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864654 | 2 |
| C2×Q8×D271 | 2 |
| #22576159 | 2 |
| #22576146 | 2 |
| #22576145 | 2 |
| #22576142 | 2 |
| #22576140 | 2 |
| #22576139 | 2 |
| #22576136 | 2 |
| #22576118 | 2 |
| C22⋊Q8×C271 | 2 |
| #536 | 271 |