Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
992 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #22599347 | C2 | semidirect |
| 3. #22587645 | C2 | semidirect |
| 4. #22586975 | C2 | semidirect |
| 5. #22586950 | C2 | semidirect |
| 6. C71×#3135 | C2 | semidirect |
| 15. #17986391 | C22 | semidirect |
| 16. #17986361 | C22 | semidirect |
| 20. #17986056 | C22 | semidirect |
| 21. #17985739 | C22 | semidirect |
| 22. #17985738 | C22 | semidirect |
| 23. #533×C71 | C22 | semidirect |
| 27. #489×C71 | C22 | semidirect |
| 29. C2×#97×C71 | C22 | semidirect |
| 173. #3135 | D71 | semidirect |
| 177. C71 | #19056 | semidirect |
| 185. #533 | C2×D71 | semidirect |
| 192. #489 | C2×D71 | semidirect |
| 198. C2×#97 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602745 | 2 |
| #22599347 | 2 |
| #22587645 | 2 |
| #22586975 | 2 |
| #22586950 | 2 |
| C71×#3135 | 2 |
| #19056 | 71 |