Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#17984864 | C2 | semidirect |
| 2. C2×#17984861 | C2 | semidirect |
| 3. #22581621 | C2 | semidirect |
| 4. #22581328 | C2 | semidirect |
| 5. #22581190 | C2 | semidirect |
| 6. #22581152 | C2 | semidirect |
| 7. #22581099 | C2 | semidirect |
| 8. #22581096 | C2 | semidirect |
| 9. #22581047 | C2 | semidirect |
| 10. C8×C22⋊D139 | C2 | semidirect |
| 11. #466×C139 | C2 | semidirect |
| 56. Dic556 | D4 | semidirect |
| 134. Dic139 | #135 | semidirect |
| 142. C139 | #3287 | semidirect |
| 149. #466 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| C2×#17984861 | 2 |
| #22581621 | 2 |
| #22581328 | 2 |
| #22581190 | 2 |
| #22581152 | 2 |
| #22581099 | 2 |
| #22581096 | 2 |
| #22581047 | 2 |
| C8×C22⋊D139 | 2 |
| #466×C139 | 2 |
| #3287 | 139 |