Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
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⋊#6157 | C2 | semidirect |
| 2. C22×#13133275 | C2 | direct (N × H) |
| 6. C22×C22⋊#6157 | C22 | semidirect |
| 7. C2×#13133275 | C22 | direct (N × H) |
| 11. C23×C22⋊D53 | C4 | semidirect |
| 13. C24×Dic53 | C4 | semidirect |
| 14. C26×C53 | C4 | semidirect |
| 18. C2×C22⋊#6157 | C23 | semidirect |
| 19. #13133275 | C23 | direct (N × H) |
| 29. C22×C22⋊D53 | C2×C4 | semidirect |
| 33. C23×Dic53 | C2×C4 | semidirect |
| 38. C25×C53 | C2×C4 | semidirect |
| 48. C24×C53 | C22×C4 | semidirect |
| 65. C2×C22⋊D53 | C22×C4 | semidirect |
| 69. C22×Dic53 | C22×C4 | semidirect |
| 71. C22⋊#6157 | C24 | semidirect |
| 79. C23×C53 | #99 | semidirect |
| 83. C23×C53 | C23×C4 | semidirect |
| 102. C2×Dic53 | C23×C4 | semidirect |
| 110. C22×C53 | C2×#99 | semidirect |
| 130. C2×C53 | C22×#99 | semidirect |
| 135. C26 | #6157 | semidirect |
| 145. C53 | C23×#99 | semidirect |
| 155. C25 | C2×#6157 | semidirect |
| 189. C24 | C22×#6157 | semidirect |
| 222. C23 | #13133275 | direct (N × H) |
| 226. C23 | C23×#6157 | semidirect |
| 248. C22 | C2×#13133275 | direct (N × H) |
| 259. C2 | C22×#13133275 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊#6157 | 2 |
| C22×#13133275 | 2 |
| C24×C22⋊D53 | 2 |
| C23×#99 | 53 |