Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #22603114 | C2 | semidirect |
| 2. C2×#17986435 | C2 | semidirect |
| 3. #22590285 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. #22589961 | C2 | semidirect |
| 6. C71×#3058 | C2 | semidirect |
| 12. #17986799 | C22 | semidirect |
| 16. #17986435 | C22 | semidirect |
| 19. C2×#14556068 | C22 | semidirect |
| 20. #17985808 | C22 | semidirect |
| 21. #17985781 | C22 | semidirect |
| 22. C22×D8×C71 | C22 | semidirect |
| 25. #469×C71 | C22 | semidirect |
| 27. #427×C71 | C22 | semidirect |
| 46. #14556150 | D4 | semidirect |
| 49. C2×Dic284 | D4 | semidirect |
| 53. C2×D568 | D4 | semidirect |
| 205. #3058 | D71 | semidirect |
| 209. C71 | #33531 | semidirect |
| 218. C22×D8 | C2×D71 | semidirect |
| 226. #469 | C2×D71 | semidirect |
| 228. #427 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22603114 | 2 |
| C2×#17986435 | 2 |
| #22590285 | 2 |
| #22590075 | 2 |
| #22589961 | 2 |
| C71×#3058 | 2 |
| #33531 | 71 |