Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1614 conjugacy classes of subgroups; only the 792 normal subgroups are shown.
This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 792 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. #20290372 | C2 | direct (N × H) |
| 7. C2×#13133272 | C4 | semidirect |
| 9. C2×C4×#88324 | C4 | semidirect |
| 21. #13133272 | C2×C4 | semidirect |
| 22. C4×#88324 | C2×C4 | semidirect |
| 86. C2×C53 | #1726 | semidirect |
| 101. C53 | C2×#1726 | semidirect |
| 167. C2 | #20290372 | 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 |
| C22×C4×#88324 | 2 |
| #20290372 | 2 |
| C2×#16810468 | 2 |
| C2×#1726 | 53 |