Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
480 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 81 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. #349×D73 | C2 | semidirect |
| 3. #338×D73 | C2 | semidirect |
| 4. #22607923 | C2 | semidirect |
| 5. #22607922 | C2 | semidirect |
| 6. #22607921 | C2 | semidirect |
| 7. C73×#1341 | C2 | semidirect |
| 20. #17988369 | C22 | semidirect |
| 23. #17988345 | C22 | semidirect |
| 25. #349×C73 | C22 | semidirect |
| 26. #338×C73 | C22 | semidirect |
| 212. D73 | #1341 | direct (N × H) |
| 219. #1341 | D73 | direct (N × H) |
| 220. C73 | C2×#1341 | semidirect |
| 236. #349 | C2×D73 | semidirect |
| 239. #338 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #469×D73 | 2 |
| #349×D73 | 2 |
| #338×D73 | 2 |
| #22607923 | 2 |
| #22607922 | 2 |
| #22607921 | 2 |
| C73×#1341 | 2 |
| C2×#1341 | 73 |