Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22599718 | C2 | semidirect |
| 2. #22598766 | C2 | semidirect |
| 3. #22587485 | C2 | semidirect |
| 4. #22587456 | C2 | semidirect |
| 5. #22587423 | C2 | semidirect |
| 6. #22587394 | C2 | semidirect |
| 7. #22587075 | C2 | semidirect |
| 8. #22586791 | C2 | semidirect |
| 9. C71×#3549 | C2 | semidirect |
| 11. #17986549 | C22 | semidirect |
| 13. #17986378 | C22 | semidirect |
| 15. #17986373 | C22 | semidirect |
| 17. #17986289 | C22 | semidirect |
| 20. #17986194 | C22 | semidirect |
| 22. #17986023 | C22 | semidirect |
| 23. C2×C4×C71⋊C8 | C22 | semidirect |
| 24. #17985748 | C22 | semidirect |
| 26. D4⋊(C71⋊C8) | C22 | semidirect |
| 27. D4⋊(C71⋊C8) | C22 | semidirect |
| 206. #3549 | D71 | semidirect |
| 215. C71 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599718 | 2 |
| #22598766 | 2 |
| #22587485 | 2 |
| #22587456 | 2 |
| #22587423 | 2 |
| #22587394 | 2 |
| #22587075 | 2 |
| #22586791 | 2 |
| C71×#3549 | 2 |
| #18686 | 71 |