Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22611340 | C2 | semidirect |
| 4. #22607757 | C2 | semidirect |
| 5. #22607756 | C2 | semidirect |
| 7. C73×#2072 | C2 | semidirect |
| 196. #2072 | D73 | semidirect |
| 200. C73 | #7821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617875 | 2 |
| #22611460 | 2 |
| #22611340 | 2 |
| #22607757 | 2 |
| #22607756 | 2 |
| #22607751 | 2 |
| C73×#2072 | 2 |
| #7821 | 73 |