Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 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. C2×C32×D73 | C2 | semidirect |
| 3. #368×D73 | C2 | semidirect |
| 4. #22608116 | C2 | semidirect |
| 5. #22608115 | C2 | semidirect |
| 6. #22608114 | C2 | semidirect |
| 7. C73×#1417 | C2 | semidirect |
| 19. C2×#14556497 | C22 | semidirect |
| 22. #17988417 | C22 | semidirect |
| 25. C2×C32×C73 | C22 | semidirect |
| 26. #368×C73 | C22 | semidirect |
| 143. D73 | #1417 | direct (N × H) |
| 150. #1417 | D73 | direct (N × H) |
| 151. C73 | C2×#1417 | semidirect |
| 167. C2×C32 | C2×D73 | semidirect |
| 170. #368 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D73 | 2 |
| C2×C32×D73 | 2 |
| #368×D73 | 2 |
| #22608116 | 2 |
| #22608115 | 2 |
| #22608114 | 2 |
| C73×#1417 | 2 |
| C2×#1417 | 73 |