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×#13133276 | C2 | direct (N × H) |
| 6. C22×C22⋊#6157 | C22 | semidirect |
| 7. C2×#13133276 | C22 | direct (N × H) |
| 8. C25×D53 | C4 | semidirect |
| 12. C23×D212 | C4 | semidirect |
| 14. C24×C4×C53 | C4 | semidirect |
| 18. C2×C22⋊#6157 | C23 | semidirect |
| 19. #13133276 | C23 | direct (N × H) |
| 25. C24×D53 | C2×C4 | semidirect |
| 33. C22×D212 | C2×C4 | semidirect |
| 38. C23×C4×C53 | C2×C4 | semidirect |
| 55. C23×D53 | C22×C4 | semidirect |
| 63. C22×C4×C53 | C22×C4 | semidirect |
| 68. C2×D212 | C22×C4 | semidirect |
| 71. C22⋊#6157 | C24 | semidirect |
| 74. C23×C53 | #99 | semidirect |
| 92. C22×D53 | C23×C4 | semidirect |
| 100. C2×C4×C53 | C23×C4 | semidirect |
| 106. C22×C53 | C2×#99 | semidirect |
| 129. C2×C53 | C22×#99 | semidirect |
| 141. C24×C4 | #6157 | semidirect |
| 145. C53 | C23×#99 | semidirect |
| 166. C23×C4 | C2×#6157 | semidirect |
| 200. C22×C4 | C22×#6157 | semidirect |
| 223. C23 | #13133276 | direct (N × H) |
| 233. C2×C4 | C23×#6157 | semidirect |
| 248. C22 | C2×#13133276 | direct (N × H) |
| 259. C2 | C22×#13133276 | 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×#13133276 | 2 |
| C24×D212 | 2 |
| C23×#99 | 53 |