Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. #22612178 | C2 | semidirect |
| 4. #22612177 | C2 | semidirect |
| 5. #22612176 | C2 | semidirect |
| 6. #22612157 | C2 | semidirect |
| 9. C73×#2245 | C2 | semidirect |
| 151. #2245 | D73 | semidirect |
| 155. C73 | #33705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620444 | 2 |
| #494×D73 | 2 |
| #22612178 | 2 |
| #22612177 | 2 |
| #22612176 | 2 |
| #22612157 | 2 |
| #22611649 | 2 |
| #22611524 | 2 |
| C73×#2245 | 2 |
| #33705 | 73 |