Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#17988625 | C2 | semidirect |
| 3. #22612140 | C2 | semidirect |
| 4. #22612123 | C2 | semidirect |
| 5. #22611719 | C2 | semidirect |
| 6. #22611644 | C2 | semidirect |
| 7. C73×#2112 | C2 | semidirect |
| 20. #17988415 | C22 | semidirect |
| 21. #17988413 | C22 | semidirect |
| 22. #17988392 | C22 | semidirect |
| 23. #17988389 | C22 | semidirect |
| 150. #2112 | D73 | semidirect |
| 151. C73 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619512 | 2 |
| C2×#17988625 | 2 |
| #22612140 | 2 |
| #22612123 | 2 |
| #22611719 | 2 |
| #22611644 | 2 |
| C73×#2112 | 2 |
| #33647 | 73 |