Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
726 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 184 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. #20289593 | C2 | semidirect |
| 5. #16811643 | C4 | semidirect |
| 18. #13133284 | C2×C4 | semidirect |
| 146. C53 | #8040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811643 | 2 |
| #20289593 | 2 |
| C2×#16810492 | 2 |
| #8040 | 53 |