Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 180. C53 | #12168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286164 | 2 |
| #20276649 | 2 |
| #20275980 | 2 |
| #20272734 | 2 |
| #20272733 | 2 |
| #20272656 | 2 |
| C53×#2188 | 2 |
| #12168 | 53 |