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 |
|---|---|---|
| 3. #20272789 | C2 | semidirect |
| 4. #20272770 | C2 | semidirect |
| 5. C53×#2252 | C2 | semidirect |
| 48. C16×C53 | SD16 | semidirect |
| 77. #2252 | D53 | semidirect |
| 97. C53 | #12454 | semidirect |
| 130. C16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276548 | 2 |
| #20274101 | 2 |
| #20272789 | 2 |
| #20272770 | 2 |
| C53×#2252 | 2 |
| #12454 | 53 |