Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
844 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 844 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. C2×#16810411 | C2 | semidirect |
| 3. C4×#13133132 | C2 | semidirect |
| 4. C53×#1800 | C2 | semidirect |
| 5. C23×D212 | C4 | semidirect |
| 12. #16810483 | C4 | semidirect |
| 13. #16810478 | C4 | semidirect |
| 39. #13133132 | D4 | semidirect |
| 194. C4×C53 | AΣL(1,𝔽16) | semidirect |
| 199. #1800 | D53 | semidirect |
| 225. C53 | #13221 | semidirect |
| 400. C4 | #16810411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278071 | 2 |
| C2×#16810411 | 2 |
| C4×#13133132 | 2 |
| C53×#1800 | 2 |
| #13221 | 53 |