Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22581581 | C2 | semidirect |
| 3. #22581255 | C2 | semidirect |
| 4. #22581251 | C2 | semidirect |
| 5. #22581241 | C2 | semidirect |
| 6. #22581231 | C2 | semidirect |
| 7. #22580995 | C2 | semidirect |
| 8. #22580989 | C2 | semidirect |
| 9. #22580981 | C2 | semidirect |
| 14. #17984841 | C22 | semidirect |
| 16. #17984833 | C22 | semidirect |
| 26. #17984776 | C22 | semidirect |
| 27. #17984775 | C22 | semidirect |
| 28. #17984775 | C22 | semidirect |
| 29. #17984774 | C22 | semidirect |
| 30. #17984773 | C22 | semidirect |
| 31. #17984773 | C22 | semidirect |
| 32. Dic139⋊C8 | C22 | semidirect |
| 33. Dic139⋊C8 | C22 | semidirect |
| 66. C2×D4×C139 | Q8 | semidirect |
| 124. C139 | #3081 | semidirect |
| 170. C2×D4 | Dic278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22581428 | 2 |
| #22581255 | 2 |
| #22581251 | 2 |
| #22581241 | 2 |
| #22581231 | 2 |
| #22580995 | 2 |
| #22580989 | 2 |
| #22580981 | 2 |
| C2×#17984763 | 2 |
| #418×C139 | 2 |
| #3081 | 139 |