Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
636 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 636 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. C2×#17988906 | C2 | semidirect |
| 3. #22614424 | C2 | semidirect |
| 4. #22610766 | C2 | semidirect |
| 5. #22610019 | C2 | semidirect |
| 6. #22607777 | C2 | semidirect |
| 7. C73×#1519 | C2 | semidirect |
| 227. #1519 | D73 | semidirect |
| 229. C73 | #9950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620679 | 2 |
| C2×#17988906 | 2 |
| #22614424 | 2 |
| #22610766 | 2 |
| #22610019 | 2 |
| #22607777 | 2 |
| C73×#1519 | 2 |
| #9950 | 73 |