Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581239 | C2 | semidirect |
| 4. #22581238 | C2 | semidirect |
| 5. #22581236 | C2 | semidirect |
| 8. #22581161 | C2 | semidirect |
| 9. #22581160 | C2 | semidirect |
| 11. #462×C139 | C2 | semidirect |
| 129. C139 | #3255 | semidirect |
| 140. #462 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #22581507 | 2 |
| #22581239 | 2 |
| #22581238 | 2 |
| #22581236 | 2 |
| #22581210 | 2 |
| #22581208 | 2 |
| #22581161 | 2 |
| #22581160 | 2 |
| #22580975 | 2 |
| #462×C139 | 2 |
| #3255 | 139 |