Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
716 conjugacy classes of subgroups; only the 380 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 380 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. #20290938 | C2 | semidirect |
| 3. C2×#16811516 | C2 | semidirect |
| 5. #16811681 | C4 | semidirect |
| 16. #13133291 | C2×C4 | semidirect |
| 18. C2×#11719910 | C2×C4 | semidirect |
| 96. C53 | #33329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291682 | 2 |
| #20290938 | 2 |
| C2×#16811516 | 2 |
| #20283141 | 2 |
| #33329 | 53 |