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. #22576153 | C2 | semidirect |
| 3. #22576150 | C2 | semidirect |
| 4. #22576146 | C2 | semidirect |
| 5. #22576144 | C2 | semidirect |
| 6. #22576141 | C2 | semidirect |
| 7. #22576137 | C2 | semidirect |
| 9. C4×Dic542 | C2 | semidirect |
| 10. C4×C22⋊D271 | C2 | semidirect |
| 11. C4×C22⋊D271 | C2 | semidirect |
| 12. #22576119 | C2 | semidirect |
| 13. #22576117 | C2 | semidirect |
| 14. C2×C4×Dic271 | C2 | semidirect |
| 15. C4×D4×C271 | C2 | semidirect |
| 103. C271 | #529 | semidirect |
| 116. C4×D4 | 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 |
| #22576146 | 2 |
| #22576144 | 2 |
| #22576141 | 2 |
| #22576137 | 2 |
| #22576132 | 2 |
| C4×Dic542 | 2 |
| C4×C22⋊D271 | 2 |
| #22576119 | 2 |
| #22576117 | 2 |
| C2×C4×Dic271 | 2 |
| C4×D4×C271 | 2 |
| #529 | 271 |