Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
3798 conjugacy classes of subgroups; only the 824 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 824 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. #22626475 | C2 | direct (N × H) |
| 2. C2×#17989535 | C2 | semidirect |
| 3. C2×#17989532 | C2 | semidirect |
| 7. #17989535 | C22 | semidirect |
| 8. #17989532 | C22 | semidirect |
| 11. C2×#14556588 | C4 | semidirect |
| 12. C2×#14556587 | C4 | semidirect |
| 13. #127×D73 | C4 | semidirect |
| 16. C2×#127×C73 | C4 | semidirect |
| 24. C22×D292 | C2×C4 | semidirect |
| 25. C22×C22⋊D73 | C2×C4 | semidirect |
| 28. C2×D4×D73 | C2×C4 | semidirect |
| 31. #14556588 | C2×C4 | semidirect |
| 32. #14556587 | C2×C4 | semidirect |
| 33. C2×C4×Dic73 | C2×C4 | semidirect |
| 34. C42×D73 | C2×C4 | semidirect |
| 36. C22×D4×C73 | C2×C4 | semidirect |
| 37. #127×C73 | C2×C4 | semidirect |
| 38. C2×C42×C73 | C2×C4 | semidirect |
| 51. C2×D292 | C22×C4 | semidirect |
| 53. C2×C22⋊D73 | C22×C4 | semidirect |
| 61. C4×Dic73 | C22×C4 | semidirect |
| 64. C2×D4×C73 | C22×C4 | semidirect |
| 66. C42×C73 | C22×C4 | semidirect |
| 109. C2×C73 | #2380 | semidirect |
| 112. D73 | #2380 | semidirect |
| 118. C73 | C2×#2380 | semidirect |
| 125. C2×#127 | #64408 | semidirect |
| 138. C22×D4 | C2×#64408 | semidirect |
| 145. #127 | C2×#64408 | semidirect |
| 151. C2×C42 | C2×#64408 | semidirect |
| 168. C2×D4 | C22×#64408 | semidirect |
| 180. C42 | C22×#64408 | semidirect |
| 225. C2 | #22626475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626475 | 2 |
| C2×#17989535 | 2 |
| C2×#17989532 | 2 |
| C2×#127×D73 | 2 |
| C2×#2380 | 73 |