Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
33214 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 3307 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. C23×C22⋊Dic73 | C2 | semidirect |
| 2. C2×#17988443 | C2 | direct (N × H) |
| 4. C24×Dic73 | C22 | semidirect |
| 6. C22×C22⋊Dic73 | C22 | semidirect |
| 7. #17988443 | C22 | direct (N × H) |
| 9. C26×C73 | C4 | semidirect |
| 13. C23×Dic73 | C23 | semidirect |
| 15. C2×C22⋊Dic73 | C23 | semidirect |
| 21. C25×C73 | C2×C4 | semidirect |
| 28. C22×Dic73 | C24 | semidirect |
| 37. C24×C73 | C22⋊C4 | semidirect |
| 40. C24×C73 | C22×C4 | semidirect |
| 53. C23×C73 | C2×C22⋊C4 | semidirect |
| 66. C22×C73 | #379 | semidirect |
| 68. C22×C73 | C22×C22⋊C4 | semidirect |
| 75. C2×C73 | C2×#379 | semidirect |
| 81. C73 | C22×#379 | semidirect |
| 83. C26 | Dic73 | semidirect |
| 95. C25 | C2×Dic73 | semidirect |
| 111. C24 | C22⋊Dic73 | semidirect |
| 114. C24 | C22×Dic73 | semidirect |
| 131. C23 | C2×C22⋊Dic73 | semidirect |
| 144. C22 | #17988443 | direct (N × H) |
| 146. C22 | C22×C22⋊Dic73 | semidirect |
| 152. C2 | C2×#17988443 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Dic73 | 2 |
| C2×#17988443 | 2 |
| C27×C73 | 2 |
| C22×#379 | 73 |