Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 216 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. C4×#13133267 | C2 | direct (N × H) |
| 4. C2×#13133267 | C4 | direct (N × H) |
| 11. #13133267 | C2×C4 | direct (N × H) |
| 36. C2×C4×C53 | C32 | semidirect |
| 51. C4×C53 | C2×C32 | semidirect |
| 57. C2×C53 | C4×C32 | semidirect |
| 67. C53 | C2×C4×C32 | semidirect |
| 93. C2×C4 | #13133267 | direct (N × H) |
| 107. C4 | C2×#13133267 | direct (N × H) |
| 110. C2 | C4×#13133267 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133267 | 2 |
| C4×#13133267 | 2 |
| C2×C4×#11719908 | 2 |
| C2×C4×C32 | 53 |