Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22581294 | C2 | semidirect |
| 3. #22581288 | C2 | semidirect |
| 4. #22581283 | C2 | semidirect |
| 5. #22581277 | C2 | semidirect |
| 6. #22581271 | C2 | semidirect |
| 7. #22581266 | C2 | semidirect |
| 8. #22580989 | C2 | semidirect |
| 9. #22580947 | C2 | semidirect |
| 10. C2×C22⋊(C139⋊C8) | C2 | semidirect |
| 11. C2×#117×C139 | C2 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. #17984775 | C22 | semidirect |
| 25. #17984773 | C22 | semidirect |
| 26. #17984773 | C22 | semidirect |
| 27. #17984765 | C22 | semidirect |
| 28. #17984765 | C22 | semidirect |
| 29. #17984762 | C22 | semidirect |
| 30. #17984762 | C22 | semidirect |
| 143. C139 | #3091 | semidirect |
| 146. C2×#117 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581464 | 2 |
| #22581294 | 2 |
| #22581288 | 2 |
| #22581283 | 2 |
| #22581277 | 2 |
| #22581271 | 2 |
| #22581266 | 2 |
| #22580989 | 2 |
| #22580947 | 2 |
| C2×C22⋊(C139⋊C8) | 2 |
| C2×#117×C139 | 2 |
| #3091 | 139 |