Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22612202 | C2 | semidirect |
| 3. #22611976 | C2 | semidirect |
| 4. #22609421 | C2 | semidirect |
| 5. #22607973 | C2 | semidirect |
| 6. #22607890 | C2 | semidirect |
| 7. C73×#1333 | C2 | semidirect |
| 14. #17988967 | C22 | semidirect |
| 21. C4⋊#11924003 | C22 | semidirect |
| 25. #346×C73 | C22 | semidirect |
| 26. #334×C73 | C22 | semidirect |
| 178. #1333 | D73 | semidirect |
| 180. C73 | #12326 | semidirect |
| 197. #346 | C2×D73 | semidirect |
| 198. #334 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621541 | 2 |
| #22612202 | 2 |
| #22611976 | 2 |
| #22609421 | 2 |
| #22607973 | 2 |
| #22607890 | 2 |
| C73×#1333 | 2 |
| #12326 | 73 |