Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C2×#17989518 | C2 | semidirect |
| 2. D73⋊#368 | C2 | semidirect |
| 3. #22625083 | C2 | semidirect |
| 4. #22625082 | C2 | semidirect |
| 8. #17989518 | C22 | semidirect |
| 11. #17989515 | C22 | semidirect |
| 135. D73 | #1417 | semidirect |
| 141. C73 | C2×#1417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| D73⋊#368 | 2 |
| #22625083 | 2 |
| #22625082 | 2 |
| #508×D73 | 2 |
| C2×#1417 | 73 |