Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 132 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. C23×#11719910 | C2 | semidirect |
| 2. C2×#16811521 | C2 | semidirect |
| 3. #20290942 | C2 | semidirect |
| 4. #20289769 | C2 | semidirect |
| 27. C2×#11719910 | D4 | semidirect |
| 126. C22×C53 | #350 | semidirect |
| 160. C53 | #12983 | semidirect |
| 265. C22 | #16811521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719910 | 2 |
| C2×#16811521 | 2 |
| #20290942 | 2 |
| #20289769 | 2 |
| #20283410 | 2 |
| #12983 | 53 |