Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
300 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #20291052 | C2 | semidirect |
| 4. #20290938 | C2 | semidirect |
| 5. #20289770 | C2 | semidirect |
| 6. #20289766 | C2 | semidirect |
| 160. C53 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291052 | 2 |
| #20290957 | 2 |
| C2×#16811521 | 2 |
| #20290938 | 2 |
| #20289770 | 2 |
| #20289766 | 2 |
| #20274518 | 2 |
| #13126 | 53 |