Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 5. #16811549 | C4 | semidirect |
| 7. C2×#13133123 | C4 | semidirect |
| 9. C2×C32×C53 | C4 | semidirect |
| 63. C2×C32 | #6157 | semidirect |
| 66. C53 | #7471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811549 | 2 |
| C2×C32×D53 | 2 |
| #7471 | 53 |