Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581319 | C2 | semidirect |
| 3. #22581315 | C2 | semidirect |
| 4. #22581310 | C2 | semidirect |
| 5. #22581301 | C2 | semidirect |
| 6. #22580957 | C2 | semidirect |
| 7. #22580952 | C2 | semidirect |
| 8. #22580947 | C2 | semidirect |
| 9. C2×#17984762 | C2 | semidirect |
| 10. #22580909 | C2 | semidirect |
| 11. #544×C139 | C2 | semidirect |
| 21. #17984765 | C22 | semidirect |
| 22. #17984765 | C22 | semidirect |
| 23. #17984765 | C22 | semidirect |
| 28. #17984762 | C22 | semidirect |
| 29. #17984762 | C22 | semidirect |
| 30. #17984762 | C22 | semidirect |
| 31. #17984753 | C22 | semidirect |
| 32. C4×C139⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C139 | C22 | semidirect |
| 36. #125×C139 | C22 | semidirect |
| 135. C139 | #3136 | semidirect |
| 137. #544 | D139 | semidirect |
| 153. C4⋊Q8 | C2×D139 | semidirect |
| 156. #125 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581522 | 2 |
| #22581319 | 2 |
| #22581315 | 2 |
| #22581310 | 2 |
| #22581301 | 2 |
| #22580957 | 2 |
| #22580952 | 2 |
| #22580947 | 2 |
| C2×#17984762 | 2 |
| #22580909 | 2 |
| #544×C139 | 2 |
| #3136 | 139 |