Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 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. #20283326 | C2 | semidirect |
| 3. #20276444 | C2 | semidirect |
| 4. C2×#16810431 | C2 | semidirect |
| 5. C2×C53×#504 | C2 | semidirect |
| 14. C2×#13133153 | C22 | semidirect |
| 15. #16810431 | C22 | semidirect |
| 16. #16810431 | C22 | semidirect |
| 19. C2×M32×C53 | C22 | semidirect |
| 20. C22×C16×C53 | C22 | semidirect |
| 114. C2×#504 | D53 | semidirect |
| 131. C2×M32 | C2×D53 | semidirect |
| 132. C22×C16 | C2×D53 | semidirect |
| 137. C53 | #33385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289489 | 2 |
| #20283326 | 2 |
| #20276444 | 2 |
| C2×#16810431 | 2 |
| C2×C53×#504 | 2 |
| #33385 | 53 |