Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
5838 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 5838 conjugacy classes of subgroups — too many to draw. Only its 1459 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×C4⋊Dic53 | C2 | semidirect |
| 3. C2×#16810560 | C2 | direct (N × H) |
| 4. C22×#95×C53 | C2 | semidirect |
| 8. C22×C4⋊Dic53 | C22 | semidirect |
| 11. #16810560 | C22 | direct (N × H) |
| 13. C2×#95×C53 | C22 | semidirect |
| 22. C2×C4⋊Dic53 | C23 | semidirect |
| 29. #95×C53 | C23 | semidirect |
| 72. C22×C53 | #399 | semidirect |
| 88. C22×#95 | D53 | semidirect |
| 89. C2×C53 | C2×#399 | semidirect |
| 102. C2×#95 | C2×D53 | semidirect |
| 103. C53 | C22×#399 | semidirect |
| 119. #95 | C22×D53 | semidirect |
| 165. C22 | #16810560 | direct (N × H) |
| 175. C2 | C2×#16810560 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic53 | 2 |
| C23×#11719921 | 2 |
| C2×#16810560 | 2 |
| C22×#95×C53 | 2 |
| C22×#399 | 53 |