Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 144 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. #20291047 | C2 | semidirect |
| 3. #20289762 | C2 | semidirect |
| 138. C53 | #12786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291047 | 2 |
| C2×#16811519 | 2 |
| #20289762 | 2 |
| C2×#16810579 | 2 |
| #12786 | 53 |