Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20289881 | C2 | semidirect |
| 4. #20289880 | C2 | semidirect |
| 14. #16810457 | C4 | semidirect |
| 16. C32×D53 | C4 | semidirect |
| 17. C53×M64 | C4 | semidirect |
| 31. #13133123 | C2×C4 | semidirect |
| 33. C32×C53 | C2×C4 | semidirect |
| 85. D53 | #1426 | semidirect |
| 91. M64 | #6157 | semidirect |
| 98. C53 | C2×#1426 | semidirect |
| 114. C32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#368 | 2 |
| C2×#16811550 | 2 |
| #20289881 | 2 |
| #20289880 | 2 |
| M64×D53 | 2 |
| C2×#1426 | 53 |