Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283632 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. #20275623 | C2 | semidirect |
| 5. #20272826 | C2 | semidirect |
| 6. #20272800 | C2 | semidirect |
| 7. C53×#2148 | C2 | semidirect |
| 11. #16811058 | C4 | semidirect |
| 168. #2148 | D53 | semidirect |
| 199. C53 | #13032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811058 | 2 |
| #20283632 | 2 |
| C2×#16810437 | 2 |
| #20275623 | 2 |
| #20272826 | 2 |
| #20272800 | 2 |
| C53×#2148 | 2 |
| #13032 | 53 |