Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 116 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. C22×#13133291 | C2 | semidirect |
| 2. C2×#16811522 | C2 | semidirect |
| 3. #20290942 | C2 | semidirect |
| 4. #20289770 | C2 | semidirect |
| 27. C2×#11719910 | D4 | semidirect |
| 160. C53 | #12984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133291 | 2 |
| C2×#16811522 | 2 |
| #20290942 | 2 |
| #20289770 | 2 |
| #20283405 | 2 |
| #12984 | 53 |