Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 159 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. C4×#13133153 | C2 | semidirect |
| 4. #20272811 | C2 | semidirect |
| 5. C2×C4×C16×C53 | C2 | semidirect |
| 15. #16810431 | C4 | direct (N × H) |
| 34. #13133153 | C2×C4 | semidirect |
| 46. C2×C16×C53 | C2×C4 | semidirect |
| 112. C4×C53 | #359 | semidirect |
| 120. C2×C4×C16 | D53 | semidirect |
| 141. C53 | C4×#359 | semidirect |
| 160. C2×C16 | C4×D53 | semidirect |
| 235. C4 | #16810431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133239 | 2 |
| C2×#16810431 | 2 |
| C4×#13133153 | 2 |
| #20272811 | 2 |
| C2×C4×C16×C53 | 2 |
| C4×#359 | 53 |