Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
370 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20291058 | C2 | semidirect |
| 3. #20291056 | C2 | semidirect |
| 5. #20289770 | C2 | semidirect |
| 6. #20289769 | C2 | semidirect |
| 166. C53 | #12916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291684 | 2 |
| #20291058 | 2 |
| #20291056 | 2 |
| #20290947 | 2 |
| #20289770 | 2 |
| #20289769 | 2 |
| #20274514 | 2 |
| #12916 | 53 |