Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #22581682 | C2 | semidirect |
| 3. #22581347 | C2 | semidirect |
| 5. #22581176 | C2 | semidirect |
| 6. #22581164 | C2 | semidirect |
| 7. #22581159 | C2 | semidirect |
| 9. #22581055 | C2 | semidirect |
| 10. C4×Dic556 | C2 | semidirect |
| 11. #446×C139 | C2 | semidirect |
| 121. C139 | #3400 | semidirect |
| 131. #446 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581682 | 2 |
| #22581347 | 2 |
| #22581326 | 2 |
| #22581176 | 2 |
| #22581164 | 2 |
| #22581159 | 2 |
| #22581154 | 2 |
| #22581055 | 2 |
| C4×Dic556 | 2 |
| #446×C139 | 2 |
| #3400 | 139 |