Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984873 | C2 | semidirect |
| 2. C2×#17984872 | C2 | semidirect |
| 4. C22×#14555775 | C2 | semidirect |
| 5. #22581529 | C2 | semidirect |
| 6. #22581348 | C2 | semidirect |
| 7. #22581345 | C2 | semidirect |
| 8. #22581335 | C2 | semidirect |
| 9. #22581332 | C2 | semidirect |
| 10. #22580909 | C2 | semidirect |
| 11. #536×C139 | C2 | semidirect |
| 143. C139 | #3156 | semidirect |
| 150. #536 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984873 | 2 |
| C2×#17984872 | 2 |
| C2×#17984862 | 2 |
| C22×#14555775 | 2 |
| #22581529 | 2 |
| #22581348 | 2 |
| #22581345 | 2 |
| #22581335 | 2 |
| #22581332 | 2 |
| #22580909 | 2 |
| #536×C139 | 2 |
| #3156 | 139 |