Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#17984861 | C2 | semidirect |
| 2. C22×Dic556 | C2 | semidirect |
| 3. #22581609 | C2 | semidirect |
| 4. #22581336 | C2 | semidirect |
| 5. #22581195 | C2 | semidirect |
| 6. #22581174 | C2 | semidirect |
| 7. #22581116 | C2 | semidirect |
| 8. #22581091 | C2 | semidirect |
| 9. #22581047 | C2 | semidirect |
| 10. C8×C22⋊D139 | C2 | semidirect |
| 11. #466×C139 | C2 | semidirect |
| 55. Dic556 | D4 | semidirect |
| 116. C22×C139 | #135 | semidirect |
| 136. C139 | #3285 | semidirect |
| 143. #466 | D139 | semidirect |
| 256. C22 | #17984861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984861 | 2 |
| C22×Dic556 | 2 |
| #22581609 | 2 |
| #22581336 | 2 |
| #22581195 | 2 |
| #22581174 | 2 |
| #22581116 | 2 |
| #22581091 | 2 |
| #22581047 | 2 |
| C8×C22⋊D139 | 2 |
| #466×C139 | 2 |
| #3285 | 139 |