Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
506 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 3. #20289920 | C2 | semidirect |
| 4. #20289554 | C2 | semidirect |
| 26. C2×#11719940 | C8 | semidirect |
| 30. C22×#88324 | C8 | semidirect |
| 181. C53 | #8156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811587 | 2 |
| #20289947 | 2 |
| #20289920 | 2 |
| #20289554 | 2 |
| #20273026 | 2 |
| #8156 | 53 |