Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
270 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 126. C53 | #7231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290594 | 2 |
| #20274752 | 2 |
| #7231 | 53 |