Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 128 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×#16811516 | C2 | semidirect |
| 3. #20289759 | C2 | semidirect |
| 6. #16811520 | C4 | semidirect |
| 17. #13133291 | C2×C4 | semidirect |
| 136. C53 | #12607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811520 | 2 |
| C2×#16811516 | 2 |
| #20289759 | 2 |
| C2×C4×#11719912 | 2 |
| #12607 | 53 |