Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1078 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22596650 | C2 | semidirect |
| 3. #22589755 | C2 | semidirect |
| 4. #22589487 | C2 | semidirect |
| 5. #22589037 | C2 | semidirect |
| 6. #22588427 | C2 | semidirect |
| 8. C71×#1749 | C2 | semidirect |
| 10. C2×#14556120 | C22 | semidirect |
| 18. #17985897 | C22 | semidirect |
| 21. #17985865 | C22 | semidirect |
| 23. #17985762 | C22 | semidirect |
| 24. #17985762 | C22 | semidirect |
| 27. C2×#97×C71 | C22 | semidirect |
| 28. #336×C71 | C22 | semidirect |
| 188. #1749 | D71 | semidirect |
| 189. C71 | #29110 | semidirect |
| 198. C2×#97 | C2×D71 | semidirect |
| 209. #336 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596650 | 2 |
| C2×#17985901 | 2 |
| #22589755 | 2 |
| #22589487 | 2 |
| #22589037 | 2 |
| #22588427 | 2 |
| #22588272 | 2 |
| C71×#1749 | 2 |
| #29110 | 71 |