Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. C4×#13133149 | C2 | semidirect |
| 3. #20272725 | C2 | semidirect |
| 4. C53×#2163 | C2 | semidirect |
| 6. #16811028 | C4 | semidirect |
| 7. #16811000 | C4 | semidirect |
| 12. C4×D424 | C4 | semidirect |
| 122. #2163 | D53 | semidirect |
| 145. C53 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| C4×#13133149 | 2 |
| #20272725 | 2 |
| C53×#2163 | 2 |
| #11744 | 53 |