Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
| 4. #22607989 | C2 | semidirect |
| 5. #22607911 | C2 | semidirect |
| 7. C73×#2252 | C2 | semidirect |
| 122. #2252 | D73 | semidirect |
| 128. C73 | #12411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622800 | 2 |
| #22612075 | 2 |
| #22609332 | 2 |
| #22607989 | 2 |
| #22607911 | 2 |
| #22607893 | 2 |
| C73×#2252 | 2 |
| #12411 | 73 |