Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 2. #20276617 | C2 | semidirect |
| 3. #20274076 | C2 | semidirect |
| 4. #20274072 | C2 | semidirect |
| 5. #20272786 | C2 | semidirect |
| 6. #20272762 | C2 | semidirect |
| 7. C53×#1361 | C2 | semidirect |
| 71. #11719908 | SD16 | semidirect |
| 90. Dic106 | D16 | semidirect |
| 118. #1361 | D53 | semidirect |
| 139. C53 | #12439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276964 | 2 |
| #20276617 | 2 |
| #20274076 | 2 |
| #20274072 | 2 |
| #20272786 | 2 |
| #20272762 | 2 |
| C53×#1361 | 2 |
| #12439 | 53 |