Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #20276990 | C2 | semidirect |
| 4. #20272771 | C2 | semidirect |
| 5. C53×#1372 | C2 | semidirect |
| 48. C16×C53 | SD16 | semidirect |
| 80. #1372 | D53 | semidirect |
| 97. C53 | #12454 | semidirect |
| 130. C16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| #20276548 | 2 |
| #20274105 | 2 |
| #20272771 | 2 |
| C53×#1372 | 2 |
| #12454 | 53 |