Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
19742 conjugacy classes of subgroups; only the 10859 normal subgroups are shown.
This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 10859 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 |
|---|---|---|
| 3. C23×#11719919 | C2 | direct (N × H) |
| 6. C24×Dic53 | C4 | semidirect |
| 9. C22×#11719919 | C22 | direct (N × H) |
| 14. C23×Dic53 | C2×C4 | semidirect |
| 17. C2×#11719919 | C23 | direct (N × H) |
| 24. C24×C53 | C4⋊C4 | semidirect |
| 32. C22×Dic53 | C22×C4 | semidirect |
| 35. #11719919 | C24 | direct (N × H) |
| 36. C23×C53 | C2×C4⋊C4 | semidirect |
| 44. C2×Dic53 | C23×C4 | semidirect |
| 48. C22×C53 | C22×C4⋊C4 | semidirect |
| 55. Dic53 | C24×C4 | semidirect |
| 60. C2×C53 | C23×C4⋊C4 | semidirect |
| 72. C53 | C24×C4⋊C4 | semidirect |
| 84. C24 | #11719919 | direct (N × H) |
| 96. C23 | C2×#11719919 | direct (N × H) |
| 107. C22 | C22×#11719919 | direct (N × H) |
| 115. C2 | C23×#11719919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic53 | 2 |
| C23×#11719919 | 2 |
| C25×C4×C53 | 2 |
| C24×C4⋊C4 | 53 |