Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22612013 | C2 | semidirect |
| 3. #22612012 | C2 | semidirect |
| 4. #22609537 | C2 | semidirect |
| 5. #22607967 | C2 | semidirect |
| 6. #22607905 | C2 | semidirect |
| 7. C73×#1335 | C2 | semidirect |
| 12. #17988967 | C22 | semidirect |
| 19. #17988408 | C22 | semidirect |
| 23. #364×C73 | C22 | semidirect |
| 24. C82×C73 | C22 | semidirect |
| 151. #1335 | D73 | semidirect |
| 152. C73 | #12312 | semidirect |
| 166. #364 | C2×D73 | semidirect |
| 169. C82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621731 | 2 |
| #22612013 | 2 |
| #22612012 | 2 |
| #22609537 | 2 |
| #22607967 | 2 |
| #22607905 | 2 |
| C73×#1335 | 2 |
| #12312 | 73 |