Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
3366 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#14556679 | C2 | semidirect |
| 3. C4×#14556678 | C2 | semidirect |
| 4. #22626491 | C2 | semidirect |
| 5. C4×D73⋊M16 | C2 | semidirect |
| 6. C2×C4×#11924036 | C2 | semidirect |
| 9. D73⋊#131 | C4 | direct (N × H) |
| 13. #17989552 | C22 | semidirect |
| 14. #17989551 | C22 | semidirect |
| 15. C4×#11924038 | C22 | semidirect |
| 16. C4×#11924037 | C22 | semidirect |
| 21. C4×#11924036 | C22 | semidirect |
| 22. C2×C4×#10596833 | C22 | semidirect |
| 34. #14556679 | C2×C4 | semidirect |
| 35. #14556678 | C2×C4 | semidirect |
| 37. D73⋊M16 | C2×C4 | semidirect |
| 39. C2×#11924036 | C2×C4 | semidirect |
| 83. #11924038 | C22×C4 | semidirect |
| 84. #11924037 | C22×C4 | semidirect |
| 87. #11924036 | C22×C4 | semidirect |
| 88. C2×#10596833 | C22×C4 | semidirect |
| 159. C4×D73 | #131 | semidirect |
| 176. C4×C73 | C2×#131 | semidirect |
| 179. Dic73 | C2×#131 | semidirect |
| 186. D73 | C4×#131 | semidirect |
| 194. C73 | C2×C4×#131 | semidirect |
| 367. C4 | D73⋊#131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D73⋊#131 | 2 |
| C4×#14556679 | 2 |
| C4×#14556678 | 2 |
| #22626491 | 2 |
| C4×D73⋊M16 | 2 |
| C2×C4×#11924036 | 2 |
| C4×#41×D73 | 2 |
| C2×C4×#131 | 73 |