Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
636 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 391 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 |
|---|---|---|
| 3. #20276488 | C2 | semidirect |
| 4. C2×#16810446 | C2 | semidirect |
| 16. C53×#504 | C4 | semidirect |
| 35. M32×C53 | C2×C4 | semidirect |
| 37. C2×C16×C53 | C2×C4 | semidirect |
| 92. #504 | Dic53 | semidirect |
| 101. C53 | #33404 | semidirect |
| 113. M32 | C2×Dic53 | semidirect |
| 115. C2×C16 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283326 | 2 |
| #20283310 | 2 |
| #20276488 | 2 |
| C2×#16810446 | 2 |
| C53×#3407 | 2 |
| #33404 | 53 |