Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #22623084 | C2 | semidirect |
| 2. #22623072 | C2 | semidirect |
| 3. #22612251 | C2 | semidirect |
| 4. #22612246 | C2 | semidirect |
| 5. #22612240 | C2 | semidirect |
| 6. C2×#17988426 | C2 | semidirect |
| 7. C73×#2258 | C2 | semidirect |
| 13. #17989019 | C22 | semidirect |
| 14. C2×Dic584 | C22 | semidirect |
| 16. Dic1168 | C22 | semidirect |
| 17. #17988426 | C22 | semidirect |
| 18. #17988426 | C22 | semidirect |
| 19. #17988426 | C22 | semidirect |
| 20. D2336 | C22 | semidirect |
| 22. M64×C73 | C22 | semidirect |
| 23. C2×C32×C73 | C22 | semidirect |
| 102. #2258 | D73 | semidirect |
| 103. C73 | #33983 | semidirect |
| 118. M64 | C2×D73 | semidirect |
| 119. C2×C32 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623084 | 2 |
| #22623072 | 2 |
| #22612251 | 2 |
| #22612246 | 2 |
| #22612240 | 2 |
| C2×#17988426 | 2 |
| C73×#2258 | 2 |
| #33983 | 73 |