Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17984108 | C2 | semidirect |
| 2. C2×#17984096 | C2 | semidirect |
| 3. #22577984 | C2 | semidirect |
| 4. #22577981 | C2 | semidirect |
| 5. #22577660 | C2 | semidirect |
| 6. #22577655 | C2 | semidirect |
| 7. #22577635 | C2 | semidirect |
| 8. #22577631 | C2 | semidirect |
| 9. C2×#17984019 | C2 | semidirect |
| 10. #22577405 | C2 | semidirect |
| 11. #417×C137 | C2 | semidirect |
| 63. C2×#11764040 | D4 | semidirect |
| 152. C137 | #3060 | semidirect |
| 164. #417 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984108 | 2 |
| C2×#17984096 | 2 |
| #22577984 | 2 |
| #22577981 | 2 |
| #22577660 | 2 |
| #22577655 | 2 |
| #22577635 | 2 |
| #22577631 | 2 |
| C2×#17984019 | 2 |
| #22577405 | 2 |
| #417×C137 | 2 |
| #3060 | 137 |