Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1806 conjugacy classes of subgroups; only the 480 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 480 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×#16811468 | C2 | direct (N × H) |
| 7. #16811468 | C22 | direct (N × H) |
| 38. C23×C4×C53 | C8 | semidirect |
| 52. C22×C4×C53 | C2×C8 | semidirect |
| 93. C2×C4×C53 | C22×C8 | semidirect |
| 115. C22×C53 | #324 | semidirect |
| 133. C2×C53 | C2×#324 | semidirect |
| 148. C53 | C22×#324 | semidirect |
| 162. C23×C4 | #88324 | semidirect |
| 202. C22×C4 | C2×#88324 | semidirect |
| 239. C2×C4 | C22×#88324 | semidirect |
| 248. C22 | #16811468 | direct (N × H) |
| 263. C2 | C2×#16811468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#88324 | 2 |
| C2×#16811468 | 2 |
| C23×C4⋊Dic53 | 2 |
| C22×#324 | 53 |