Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984875 | C2 | semidirect |
| 2. C2×#17984862 | C2 | semidirect |
| 3. C22×#14555773 | C2 | semidirect |
| 4. #22581524 | C2 | semidirect |
| 5. #22581520 | C2 | semidirect |
| 6. #22581344 | C2 | semidirect |
| 7. #22581341 | C2 | semidirect |
| 8. #22581336 | C2 | semidirect |
| 9. #22581324 | C2 | semidirect |
| 10. #22580911 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 16. C2×Dic556 | C22 | semidirect |
| 17. C2×#14555775 | C22 | semidirect |
| 18. C2×#14555774 | C22 | semidirect |
| 22. C2×#14555773 | C22 | semidirect |
| 23. C2×#14555772 | C22 | semidirect |
| 24. C2×#14555770 | C22 | semidirect |
| 26. #17984840 | C22 | semidirect |
| 29. #17984829 | C22 | semidirect |
| 35. #17984752 | C22 | semidirect |
| 36. C8×Dic139 | C22 | semidirect |
| 63. C2×C139⋊C8 | D4 | semidirect |
| 86. M16×C139 | D4 | semidirect |
| 148. C139 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D139 | semidirect |
| 226. M16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984875 | 2 |
| C2×#17984862 | 2 |
| C22×#14555773 | 2 |
| #22581524 | 2 |
| #22581520 | 2 |
| #22581344 | 2 |
| #22581341 | 2 |
| #22581336 | 2 |
| #22581324 | 2 |
| #22580911 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #3154 | 139 |