Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22610899 | C2 | semidirect |
| 4. C2×#17988328 | C2 | semidirect |
| 6. #22607812 | C2 | semidirect |
| 7. C73×#1836 | C2 | semidirect |
| 210. #1836 | D73 | semidirect |
| 214. C73 | #10426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617983 | 2 |
| #22610899 | 2 |
| #22610745 | 2 |
| C2×#17988328 | 2 |
| C2×#17988326 | 2 |
| #22607812 | 2 |
| C73×#1836 | 2 |
| #10426 | 73 |