Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. C2×#13133132 | C4 | semidirect |
| 8. C2×C22⋊C8×C53 | C4 | semidirect |
| 95. C2×C22⋊C8 | Dic53 | semidirect |
| 97. C53 | #7305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274633 | 2 |
| C53×#1780 | 2 |
| #7305 | 53 |