Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1330 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 1. C2×#16811013 | C2 | semidirect |
| 2. #20274004 | C2 | direct (N × H) |
| 3. C2×#16810363 | C2 | semidirect |
| 4. C2×C53×H(3,𝔽4) | C2 | semidirect |
| 7. C2×#13133214 | C22 | semidirect |
| 9. #16811013 | C22 | semidirect |
| 10. C2×#13133128 | C22 | semidirect |
| 11. #16810363 | C22 | semidirect |
| 13. C53×H(3,𝔽4) | C22 | semidirect |
| 24. #13133214 | C23 | semidirect |
| 26. #13133128 | C23 | semidirect |
| 104. C2×H(3,𝔽4) | D53 | semidirect |
| 109. C2×C53 | #1655 | semidirect |
| 115. H(3,𝔽4) | C2×D53 | semidirect |
| 124. C53 | C2×#1655 | semidirect |
| 213. C2 | #20274004 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811013 | 2 |
| #20274004 | 2 |
| C2×#16810363 | 2 |
| C2×C53×H(3,𝔽4) | 2 |
| C2×#1655 | 53 |