Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
814 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 251 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. #20276967 | C2 | direct (N × H) |
| 81. C2×C4×C53 | Q32 | semidirect |
| 101. C4×C53 | C2×Q32 | semidirect |
| 110. C2×C53 | #2247 | semidirect |
| 128. C53 | C2×#2247 | semidirect |
| 194. C2×C4 | #13133163 | semidirect |
| 209. C4 | C2×#13133163 | semidirect |
| 212. C2 | #20276967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133163 | 2 |
| C2×#16811003 | 2 |
| #20276967 | 2 |
| C2×C4×#11719908 | 2 |
| C2×C53×#494 | 2 |
| C2×#2247 | 53 |