Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22601481 | C2 | semidirect |
| 2. #22590653 | C2 | semidirect |
| 3. #22590652 | C2 | semidirect |
| 4. #22590647 | C2 | semidirect |
| 5. C2×#17985834 | C2 | semidirect |
| 6. #22590634 | C2 | semidirect |
| 7. C71×#3415 | C2 | semidirect |
| 10. #17986431 | C22 | semidirect |
| 11. C2×D1136 | C22 | semidirect |
| 12. #17985839 | C22 | semidirect |
| 13. #17985837 | C22 | semidirect |
| 14. #17985836 | C22 | semidirect |
| 15. #17985834 | C22 | semidirect |
| 16. #17985834 | C22 | semidirect |
| 17. #17985833 | C22 | semidirect |
| 18. C2×C71⋊C32 | C22 | semidirect |
| 21. #508×C71 | C22 | semidirect |
| 22. C2×D16×C71 | C22 | semidirect |
| 98. #3415 | D71 | semidirect |
| 104. C71 | #33982 | semidirect |
| 110. #508 | C2×D71 | semidirect |
| 112. C2×D16 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601481 | 2 |
| #22590653 | 2 |
| #22590652 | 2 |
| #22590647 | 2 |
| C2×#17985834 | 2 |
| #22590634 | 2 |
| C71×#3415 | 2 |
| #33982 | 71 |