Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20276918 | C2 | semidirect |
| 3. #20276898 | C2 | semidirect |
| 4. #20276145 | C2 | semidirect |
| 5. #20272726 | C2 | semidirect |
| 6. #20272638 | C2 | semidirect |
| 7. C53×#1347 | C2 | semidirect |
| 167. #1347 | D53 | semidirect |
| 195. C53 | #12283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285502 | 2 |
| #20276918 | 2 |
| #20276898 | 2 |
| #20276145 | 2 |
| #20272726 | 2 |
| #20272638 | 2 |
| C53×#1347 | 2 |
| #12283 | 53 |