Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 360 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×#16811555 | C2 | direct (N × H) |
| 2. C22×#13133267 | C2 | semidirect |
| 4. #16811555 | C22 | direct (N × H) |
| 5. C2×#13133267 | C22 | semidirect |
| 11. #13133267 | C23 | semidirect |
| 48. C22×C53 | M64 | semidirect |
| 58. C2×C53 | C2×M64 | semidirect |
| 67. C53 | C22×M64 | semidirect |
| 104. C22 | #16811555 | direct (N × H) |
| 111. C2 | C2×#16811555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811555 | 2 |
| C22×#13133267 | 2 |
| C23×#11719908 | 2 |
| C22×M64 | 53 |