Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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. C16×D212 | C2 | semidirect |
| 3. #20272785 | C2 | semidirect |
| 4. #20272671 | C2 | semidirect |
| 5. C8×C16×C53 | C2 | semidirect |
| 42. D424 | C16 | direct (N × H) |
| 47. C16×C53 | D8 | semidirect |
| 55. D212 | C2×C16 | semidirect |
| 61. C8×C53 | C2×C16 | semidirect |
| 80. C8×C16 | D53 | semidirect |
| 95. C53 | C16×D8 | semidirect |
| 128. C16 | D424 | direct (N × H) |
| 142. C8 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D212 | 2 |
| C8×D424 | 2 |
| #20272785 | 2 |
| #20272671 | 2 |
| C8×C16×C53 | 2 |
| C16×D8 | 53 |