Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20276499 | C2 | semidirect |
| 3. #20272917 | C2 | semidirect |
| 4. #20272915 | C2 | semidirect |
| 5. #20272894 | C2 | semidirect |
| 6. #20272894 | C2 | semidirect |
| 7. C53×C22⋊C32 | C2 | semidirect |
| 89. C22⋊C32 | D53 | semidirect |
| 106. C53 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276801 | 2 |
| #20276499 | 2 |
| #20272917 | 2 |
| #20272915 | 2 |
| #20272894 | 2 |
| C53×C22⋊C32 | 2 |
| #13713 | 53 |