Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22611705 | C2 | semidirect |
| 3. C2×#17988411 | C2 | semidirect |
| 6. #22608037 | C2 | semidirect |
| 7. C73×#1388 | C2 | semidirect |
| 9. #17989005 | C4 | semidirect |
| 143. #1388 | D73 | semidirect |
| 145. C73 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623033 | 2 |
| #22611705 | 2 |
| C2×#17988411 | 2 |
| #22609987 | 2 |
| #22609986 | 2 |
| #22608037 | 2 |
| C73×#1388 | 2 |
| #12833 | 73 |