Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 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. #22602745 | C2 | semidirect |
| 2. #22599718 | C2 | semidirect |
| 3. #22587483 | C2 | semidirect |
| 4. #22587454 | C2 | semidirect |
| 5. #22587421 | C2 | semidirect |
| 6. #22587392 | C2 | semidirect |
| 7. #22587075 | C2 | semidirect |
| 8. #22586792 | C2 | semidirect |
| 9. C71×#3147 | C2 | semidirect |
| 19. #17986286 | C22 | semidirect |
| 22. #17986191 | C22 | semidirect |
| 23. #17986023 | C22 | semidirect |
| 24. #17985748 | C22 | semidirect |
| 26. #17985728 | C22 | semidirect |
| 27. #17985728 | C22 | semidirect |
| 30. #532×C71 | C22 | semidirect |
| 32. #494×C71 | C22 | semidirect |
| 35. #492×C71 | C22 | semidirect |
| 36. C2×C4×C8×C71 | C22 | semidirect |
| 208. #3147 | D71 | semidirect |
| 215. C71 | #18686 | semidirect |
| 226. #532 | C2×D71 | semidirect |
| 228. #494 | C2×D71 | semidirect |
| 231. #492 | C2×D71 | semidirect |
| 238. C2×C4×C8 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602745 | 2 |
| #22599718 | 2 |
| #22587483 | 2 |
| #22587454 | 2 |
| #22587421 | 2 |
| #22587392 | 2 |
| #22587075 | 2 |
| #22586792 | 2 |
| C71×#3147 | 2 |
| #18686 | 71 |