Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2846 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 2846 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 |
|---|---|---|
| 2. C22×#13133287 | C2 | direct (N × H) |
| 7. C2×#13133287 | C22 | direct (N × H) |
| 16. #13133287 | C23 | direct (N × H) |
| 48. C23×C53 | #108 | semidirect |
| 67. C22×C53 | C2×#108 | semidirect |
| 80. C2×C53 | C22×#108 | semidirect |
| 93. C53 | C23×#108 | semidirect |
| 133. C23 | #13133287 | direct (N × H) |
| 151. C22 | C2×#13133287 | direct (N × H) |
| 159. C2 | C22×#13133287 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719936 | 2 |
| C22×#13133287 | 2 |
| C23×C8×D53 | 2 |
| C23×#108 | 53 |