Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 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. #22623072 | C2 | semidirect |
| 2. #22621731 | C2 | semidirect |
| 3. #22612181 | C2 | semidirect |
| 4. #22612051 | C2 | semidirect |
| 5. #22612008 | C2 | semidirect |
| 6. #22611890 | C2 | semidirect |
| 7. #22611813 | C2 | semidirect |
| 8. C73×#2170 | C2 | semidirect |
| 9. #17989392 | C22 | semidirect |
| 12. #17989025 | C22 | semidirect |
| 16. C2×D1168 | C22 | semidirect |
| 17. C2×D1168 | C22 | semidirect |
| 18. #17988964 | C22 | semidirect |
| 20. #17988857 | C22 | semidirect |
| 22. #17988705 | C22 | semidirect |
| 23. #17988417 | C22 | semidirect |
| 24. #17988401 | C22 | semidirect |
| 25. #17988395 | C22 | semidirect |
| 26. #504×C73 | C22 | semidirect |
| 28. #364×C73 | C22 | semidirect |
| 29. #350×C73 | C22 | semidirect |
| 30. C4×C16×C73 | C22 | semidirect |
| 45. Dic584 | D4 | semidirect |
| 47. #14556536 | D4 | semidirect |
| 52. D1168 | D4 | semidirect |
| 150. #2170 | D73 | semidirect |
| 151. C73 | #33858 | semidirect |
| 161. #504 | C2×D73 | semidirect |
| 169. #364 | C2×D73 | semidirect |
| 172. #350 | C2×D73 | semidirect |
| 173. C4×C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623072 | 2 |
| #22621731 | 2 |
| #22612181 | 2 |
| #22612051 | 2 |
| #22612008 | 2 |
| #22611890 | 2 |
| #22611813 | 2 |
| C73×#2170 | 2 |
| #33858 | 73 |