Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 160 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. #20289634 | C2 | direct (N × H) |
| 19. C2×#11719910 | C8 | semidirect |
| 54. #11719910 | C2×C8 | semidirect |
| 91. C2×C53 | #1313 | semidirect |
| 107. C53 | C2×#1313 | semidirect |
| 177. C2 | #20289634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811512 | 2 |
| C2×#16811464 | 2 |
| #20289634 | 2 |
| C2×#16810398 | 2 |
| C2×#1313 | 53 |