Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3678 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C2×#16810491 | C2 | direct (N × H) |
| 5. #16810491 | C22 | direct (N × H) |
| 8. C22×C42×C53 | C4 | semidirect |
| 17. C2×C42×C53 | C2×C4 | semidirect |
| 29. C42×C53 | C22×C4 | semidirect |
| 41. C22×C53 | #383 | semidirect |
| 51. C2×C53 | C2×#383 | semidirect |
| 56. C22×C42 | Dic53 | semidirect |
| 60. C53 | C22×#383 | semidirect |
| 67. C2×C42 | C2×Dic53 | semidirect |
| 80. C42 | C22×Dic53 | semidirect |
| 91. C22 | #16810491 | direct (N × H) |
| 98. C2 | C2×#16810491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| C22×#13133124 | 2 |
| C23×C42×C53 | 2 |
| C22×#383 | 53 |