Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 3. #22580908 | C2 | semidirect |
| 4. C2×#17984752 | C2 | semidirect |
| 5. #22580717 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 12. #17984769 | C4 | semidirect |
| 13. #17984766 | C4 | semidirect |
| 14. #17984763 | C4 | semidirect |
| 20. #131×C139 | C4 | semidirect |
| 98. C139 | #1765 | semidirect |
| 109. #131 | Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984769 | 2 |
| #22580949 | 2 |
| #22580908 | 2 |
| C2×#17984752 | 2 |
| #22580717 | 2 |
| #22580714 | 2 |
| C2×#131×C139 | 2 |
| #1765 | 139 |