Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22610882 | C2 | semidirect |
| 4. #22610775 | C2 | semidirect |
| 6. #22607833 | C2 | semidirect |
| 7. C73×#1565 | C2 | semidirect |
| 194. #1565 | D73 | semidirect |
| 197. C73 | #10503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621054 | 2 |
| #22610882 | 2 |
| #22610850 | 2 |
| #22610775 | 2 |
| #22608606 | 2 |
| #22607833 | 2 |
| C73×#1565 | 2 |
| #10503 | 73 |