Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
788 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 788 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. #22599296 | C2 | semidirect |
| 2. #22599255 | C2 | semidirect |
| 3. #22598715 | C2 | semidirect |
| 4. #22588005 | C2 | semidirect |
| 5. #22587998 | C2 | semidirect |
| 6. #22587976 | C2 | semidirect |
| 7. #22587944 | C2 | semidirect |
| 8. #22586637 | C2 | semidirect |
| 9. C71×#3184 | C2 | semidirect |
| 12. #17986378 | C22 | semidirect |
| 15. #17986371 | C22 | semidirect |
| 17. #17986349 | C22 | semidirect |
| 22. #17986345 | C22 | semidirect |
| 29. #17985721 | C22 | semidirect |
| 30. #17985720 | C22 | semidirect |
| 31. C8×C71⋊C8 | C22 | semidirect |
| 33. #498×C71 | C22 | semidirect |
| 34. #493×C71 | C22 | semidirect |
| 35. #486×C71 | C22 | semidirect |
| 172. #3184 | D71 | semidirect |
| 179. C71 | #19729 | semidirect |
| 183. #498 | C2×D71 | semidirect |
| 187. #493 | C2×D71 | semidirect |
| 196. #486 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599296 | 2 |
| #22599255 | 2 |
| #22598715 | 2 |
| #22588005 | 2 |
| #22587998 | 2 |
| #22587976 | 2 |
| #22587944 | 2 |
| #22586637 | 2 |
| C71×#3184 | 2 |
| #19729 | 71 |