Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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. C22×#14555775 | C2 | semidirect |
| 3. #22581527 | C2 | semidirect |
| 4. #22581112 | C2 | semidirect |
| 5. #22581107 | C2 | semidirect |
| 6. #22580963 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. #22580921 | C2 | semidirect |
| 9. C2×#137×C139 | C2 | semidirect |
| 140. C139 | #3011 | semidirect |
| 143. C2×#137 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984889 | 2 |
| C22×#14555775 | 2 |
| #22581527 | 2 |
| #22581112 | 2 |
| #22581107 | 2 |
| #22580963 | 2 |
| #22580949 | 2 |
| #22580921 | 2 |
| C2×#137×C139 | 2 |
| #3011 | 139 |