Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 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. #22581305 | C2 | semidirect |
| 5. #22581235 | C2 | semidirect |
| 7. #22581163 | C2 | semidirect |
| 8. #22581084 | C2 | semidirect |
| 9. #22581058 | C2 | semidirect |
| 11. Q82×C139 | C2 | semidirect |
| 116. C139 | #3369 | semidirect |
| 118. Q82 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581676 | 2 |
| #22581315 | 2 |
| #22581305 | 2 |
| #22581240 | 2 |
| #22581235 | 2 |
| #22581175 | 2 |
| #22581163 | 2 |
| #22581084 | 2 |
| #22581058 | 2 |
| C4×#14555772 | 2 |
| Q82×C139 | 2 |
| #3369 | 139 |