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×#14556649 | C2 | direct (N × H) |
| 6. C22×C22⋊#64408 | C22 | semidirect |
| 7. C2×#14556649 | C22 | direct (N × H) |
| 11. C23×C22⋊D73 | C4 | semidirect |
| 13. C24×Dic73 | C4 | semidirect |
| 14. C26×C73 | C4 | semidirect |
| 18. C2×C22⋊#64408 | C23 | semidirect |
| 19. #14556649 | C23 | direct (N × H) |
| 29. C22×C22⋊D73 | C2×C4 | semidirect |
| 33. C23×Dic73 | C2×C4 | semidirect |
| 38. C25×C73 | C2×C4 | semidirect |
| 42. C22⋊#64408 | C24 | semidirect |
| 57. C2×C22⋊D73 | C22×C4 | semidirect |
| 61. C22×Dic73 | C22×C4 | semidirect |
| 71. C24×C73 | C22×C4 | semidirect |
| 79. C23×C73 | #99 | semidirect |
| 83. C23×C73 | C23×C4 | semidirect |
| 102. C2×Dic73 | C23×C4 | semidirect |
| 109. C22×C73 | C2×#99 | semidirect |
| 127. C2×C73 | C22×#99 | semidirect |
| 134. C73 | C23×#99 | semidirect |
| 136. C26 | #64408 | semidirect |
| 155. C25 | C2×#64408 | semidirect |
| 189. C24 | C22×#64408 | semidirect |
| 222. C23 | #14556649 | direct (N × H) |
| 226. C23 | C23×#64408 | semidirect |
| 248. C22 | C2×#14556649 | direct (N × H) |
| 259. C2 | C22×#14556649 | 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×#14556649 | 2 |
| C24×C22⋊D73 | 2 |
| C23×#99 | 73 |