Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
848 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 107 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×#17988385 | C2 | semidirect |
| 3. C2×#17988384 | C2 | semidirect |
| 4. C2×#17988383 | C2 | semidirect |
| 5. #22610334 | C2 | semidirect |
| 6. #22610324 | C2 | semidirect |
| 7. C73×#1888 | C2 | semidirect |
| 11. #17989299 | C4 | semidirect |
| 256. #1888 | D73 | semidirect |
| 258. C73 | #12776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989299 | 2 |
| C2×#17988385 | 2 |
| C2×#17988384 | 2 |
| C2×#17988383 | 2 |
| #22610334 | 2 |
| #22610324 | 2 |
| C73×#1888 | 2 |
| #12776 | 73 |