Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22609446 | C2 | semidirect |
| 4. #22607983 | C2 | semidirect |
| 5. #22607914 | C2 | semidirect |
| 7. C73×#2255 | C2 | semidirect |
| 68. D584 | Q16 | semidirect |
| 137. #2255 | D73 | semidirect |
| 143. C73 | #12414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622892 | 2 |
| #22612075 | 2 |
| #22609446 | 2 |
| #22607983 | 2 |
| #22607914 | 2 |
| #22607899 | 2 |
| C73×#2255 | 2 |
| #12414 | 73 |