Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1486 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 291 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. C2×#17988376 | C2 | direct (N × H) |
| 5. C24×Dic73 | C4 | semidirect |
| 9. C2×#14556572 | C4 | semidirect |
| 13. C22×C22⋊Dic73 | C4 | semidirect |
| 16. #17988376 | C22 | direct (N × H) |
| 26. C23×Dic73 | C2×C4 | semidirect |
| 33. #14556572 | C2×C4 | semidirect |
| 40. C2×C22⋊Dic73 | C2×C4 | semidirect |
| 67. C22×Dic73 | C22×C4 | semidirect |
| 76. C22⋊Dic73 | C22×C4 | semidirect |
| 172. C22×C73 | #352 | semidirect |
| 188. C2×C73 | C2×#352 | semidirect |
| 194. C73 | C22×#352 | semidirect |
| 362. C22 | #17988376 | direct (N × H) |
| 377. C2 | C2×#17988376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556572 | 2 |
| C22×#14556508 | 2 |
| C2×#17988376 | 2 |
| C22×#99×C73 | 2 |
| C22×#352 | 73 |