Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 134. C2×Dic53 | Q32 | semidirect |
| 189. C53 | #12162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286056 | 2 |
| #20276649 | 2 |
| #20276035 | 2 |
| #20272728 | 2 |
| #20272727 | 2 |
| #20272654 | 2 |
| C53×#2188 | 2 |
| #12162 | 53 |