Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#17984119 | C2 | semidirect |
| 3. C2×Q8×Dic137 | C2 | semidirect |
| 4. #22577627 | C2 | semidirect |
| 5. #22577623 | C2 | semidirect |
| 6. #22577611 | C2 | semidirect |
| 7. #22577601 | C2 | semidirect |
| 8. #22577426 | C2 | semidirect |
| 9. #22577405 | C2 | semidirect |
| 10. #22577404 | C2 | semidirect |
| 11. C2×#137×C137 | C2 | semidirect |
| 80. C2×Q8×C137 | D4 | semidirect |
| 150. Dic137 | #137 | semidirect |
| 157. C137 | #3037 | semidirect |
| 160. C2×#137 | D137 | semidirect |
| 210. C2×Q8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| #22577949 | 2 |
| C2×Q8×Dic137 | 2 |
| #22577627 | 2 |
| #22577623 | 2 |
| #22577611 | 2 |
| #22577601 | 2 |
| #22577426 | 2 |
| #22577405 | 2 |
| #22577404 | 2 |
| C2×#137×C137 | 2 |
| #3037 | 137 |