Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#17984875 | C2 | semidirect |
| 3. C2×#17984872 | C2 | semidirect |
| 4. C2×#17984842 | C2 | semidirect |
| 5. #22581137 | C2 | direct (N × H) |
| 6. C2×#17984770 | C2 | semidirect |
| 7. C2×#17984760 | C2 | semidirect |
| 8. C2×#104×C139 | C2 | semidirect |
| 22. #17984875 | C22 | semidirect |
| 24. #17984872 | C22 | semidirect |
| 31. #17984842 | C22 | semidirect |
| 33. #17984770 | C22 | semidirect |
| 34. #17984760 | C22 | semidirect |
| 38. #104×C139 | C22 | semidirect |
| 167. C2×C139 | #456 | semidirect |
| 170. C139 | C2×#456 | semidirect |
| 178. C2×#104 | D139 | semidirect |
| 208. #104 | C2×D139 | semidirect |
| 339. C2 | #22581137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C2×#17984875 | 2 |
| C2×#17984872 | 2 |
| C2×#17984842 | 2 |
| #22581137 | 2 |
| C2×#17984770 | 2 |
| C2×#17984760 | 2 |
| C2×#104×C139 | 2 |
| C2×#456 | 139 |