Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22576153 | C2 | semidirect |
| 3. #22576150 | C2 | semidirect |
| 4. #22576150 | C2 | semidirect |
| 5. #22576145 | C2 | semidirect |
| 6. #22576143 | C2 | semidirect |
| 7. #22576142 | C2 | semidirect |
| 8. #22576142 | C2 | semidirect |
| 9. #22576136 | C2 | semidirect |
| 10. #22576136 | C2 | semidirect |
| 12. #22576122 | C2 | semidirect |
| 13. C4×C22⋊D271 | C2 | semidirect |
| 14. C4⋊C4×D271 | C2 | semidirect |
| 15. C22⋊Q8×C271 | C2 | semidirect |
| 103. C271 | #539 | semidirect |
| 115. 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 |
| #22576153 | 2 |
| #22576150 | 2 |
| #22576145 | 2 |
| #22576143 | 2 |
| #22576142 | 2 |
| #22576136 | 2 |
| #22576133 | 2 |
| #22576122 | 2 |
| C4×C22⋊D271 | 2 |
| C4⋊C4×D271 | 2 |
| C22⋊Q8×C271 | 2 |
| #539 | 271 |