Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22609332 | C2 | semidirect |
| 5. #22607909 | C2 | semidirect |
| 6. #22607895 | C2 | semidirect |
| 7. C73×#2227 | C2 | semidirect |
| 129. #2227 | D73 | semidirect |
| 134. C73 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622941 | 2 |
| #22612156 | 2 |
| #22609332 | 2 |
| #22607978 | 2 |
| #22607909 | 2 |
| #22607895 | 2 |
| C73×#2227 | 2 |
| #12385 | 73 |