Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
782 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 491 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. C2×#16810451 | C2 | direct (N × H) |
| 7. #16810451 | C22 | direct (N × H) |
| 9. C22×C16×C53 | C4 | semidirect |
| 21. C2×C16×C53 | C2×C4 | semidirect |
| 37. C16×C53 | C22×C4 | semidirect |
| 52. C22×C53 | #367 | semidirect |
| 63. C2×C53 | C2×#367 | semidirect |
| 68. C22×C16 | Dic53 | semidirect |
| 73. C53 | C22×#367 | semidirect |
| 82. C2×C16 | C2×Dic53 | semidirect |
| 100. C16 | C22×Dic53 | semidirect |
| 114. C22 | #16810451 | direct (N × H) |
| 122. C2 | C2×#16810451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133151 | 2 |
| C2×#16810451 | 2 |
| C23×C16×C53 | 2 |
| C22×#367 | 53 |