Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 17. C2×M16×C53 | C8 | semidirect |
| 23. C22×C8×C53 | C8 | semidirect |
| 124. C53 | #7190 | semidirect |
| 129. C2×M16 | #88322 | semidirect |
| 135. C22×C8 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273029 | 2 |
| C53×#1729 | 2 |
| #7190 | 53 |