Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22599081 | C2 | semidirect |
| 4. #22588003 | C2 | semidirect |
| 5. #22587998 | C2 | semidirect |
| 6. #22587997 | C2 | semidirect |
| 7. #22587953 | C2 | semidirect |
| 8. #22586643 | C2 | semidirect |
| 9. C71×#3185 | C2 | semidirect |
| 12. #17986395 | C22 | semidirect |
| 13. #17986378 | C22 | semidirect |
| 16. #17986351 | C22 | semidirect |
| 17. #17986349 | C22 | semidirect |
| 29. #17985721 | C22 | semidirect |
| 30. #17985720 | C22 | semidirect |
| 31. C8×C71⋊C8 | C22 | semidirect |
| 33. #498×C71 | C22 | semidirect |
| 34. #494×C71 | C22 | semidirect |
| 35. #487×C71 | C22 | semidirect |
| 161. #3185 | D71 | semidirect |
| 169. C71 | #19753 | semidirect |
| 174. #498 | C2×D71 | semidirect |
| 176. #494 | C2×D71 | semidirect |
| 181. #487 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599081 | 2 |
| #22598716 | 2 |
| #22598715 | 2 |
| #22588003 | 2 |
| #22587998 | 2 |
| #22587997 | 2 |
| #22587953 | 2 |
| #22586643 | 2 |
| C71×#3185 | 2 |
| #19753 | 71 |