Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
656 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22610493 | C2 | semidirect |
| 4. #22609802 | C2 | semidirect |
| 6. #22609618 | C2 | semidirect |
| 7. C73×#1840 | C2 | semidirect |
| 120. #1840 | D73 | semidirect |
| 124. C73 | #21670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613229 | 2 |
| #22610542 | 2 |
| #22610493 | 2 |
| #22609802 | 2 |
| #22609711 | 2 |
| #22609618 | 2 |
| C73×#1840 | 2 |
| #21670 | 73 |