Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
7902 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7902 conjugacy classes of subgroups — too many to draw. Only its 1208 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⋊#64408 | C2 | semidirect |
| 2. C22×#14556650 | C2 | direct (N × H) |
| 6. C22×C22⋊#64408 | C22 | semidirect |
| 7. C2×#14556650 | C22 | direct (N × H) |
| 8. C25×D73 | C4 | semidirect |
| 12. C23×D292 | C4 | semidirect |
| 14. C24×C4×C73 | C4 | semidirect |
| 18. C2×C22⋊#64408 | C23 | semidirect |
| 19. #14556650 | C23 | direct (N × H) |
| 25. C24×D73 | C2×C4 | semidirect |
| 33. C22×D292 | C2×C4 | semidirect |
| 38. C23×C4×C73 | C2×C4 | semidirect |
| 42. C22⋊#64408 | C24 | semidirect |
| 55. C23×D73 | C22×C4 | semidirect |
| 63. C2×D292 | C22×C4 | semidirect |
| 71. C22×C4×C73 | C22×C4 | semidirect |
| 74. C23×C73 | #99 | semidirect |
| 92. C22×D73 | C23×C4 | semidirect |
| 100. C2×C4×C73 | C23×C4 | semidirect |
| 105. C22×C73 | C2×#99 | semidirect |
| 126. C2×C73 | C22×#99 | semidirect |
| 134. C73 | C23×#99 | semidirect |
| 142. C24×C4 | #64408 | semidirect |
| 166. C23×C4 | C2×#64408 | semidirect |
| 200. C22×C4 | C22×#64408 | semidirect |
| 223. C23 | #14556650 | direct (N × H) |
| 233. C2×C4 | C23×#64408 | semidirect |
| 248. C22 | C2×#14556650 | direct (N × H) |
| 259. C2 | C22×#14556650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊#64408 | 2 |
| C22×#14556650 | 2 |
| C24×D292 | 2 |
| C23×#99 | 73 |