Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1158 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 320 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 |
|---|---|---|
| 3. C2×#16811480 | C2 | direct (N × H) |
| 11. #16811480 | C22 | direct (N × H) |
| 105. C22×C53 | #330 | semidirect |
| 122. C2×C53 | C2×#330 | semidirect |
| 142. C53 | C22×#330 | semidirect |
| 226. C22 | #16811480 | direct (N × H) |
| 239. C2 | C2×#16811480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133272 | 2 |
| C2×#16811480 | 2 |
| C22×#13133208 | 2 |
| C22×#330 | 53 |