Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 64. Dic212 | Q16 | semidirect |
| 123. C53 | #12446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276858 | 2 |
| #20276854 | 2 |
| #20274332 | 2 |
| #20273521 | 2 |
| #20272784 | 2 |
| #20272771 | 2 |
| C53×#1364 | 2 |
| #12446 | 53 |