Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #22581508 | C2 | semidirect |
| 3. #22581247 | C2 | semidirect |
| 4. #22581230 | C2 | semidirect |
| 5. #22581200 | C2 | semidirect |
| 6. #22581198 | C2 | semidirect |
| 7. #22581159 | C2 | semidirect |
| 8. #22581158 | C2 | semidirect |
| 9. #22581152 | C2 | semidirect |
| 10. #22580975 | C2 | semidirect |
| 11. #474×C139 | C2 | semidirect |
| 142. C139 | #3254 | semidirect |
| 148. #474 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| #22581500 | 2 |
| #22581247 | 2 |
| #22581230 | 2 |
| #22581200 | 2 |
| #22581198 | 2 |
| #22581159 | 2 |
| #22581158 | 2 |
| #22581152 | 2 |
| #22580975 | 2 |
| #474×C139 | 2 |
| #3254 | 139 |