Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22623081 | C2 | semidirect |
| 2. #22621736 | C2 | semidirect |
| 3. #22612184 | C2 | semidirect |
| 4. #22612057 | C2 | semidirect |
| 5. #22612012 | C2 | semidirect |
| 6. #22611910 | C2 | semidirect |
| 7. #22611769 | C2 | semidirect |
| 8. C73×#2178 | C2 | semidirect |
| 145. #2178 | D73 | semidirect |
| 147. C73 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623081 | 2 |
| #22621736 | 2 |
| #22612184 | 2 |
| #22612057 | 2 |
| #22612012 | 2 |
| #22611910 | 2 |
| #22611769 | 2 |
| C73×#2178 | 2 |
| #33860 | 73 |