Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 110 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. #20289825 | C2 | semidirect |
| 4. #20289824 | C2 | semidirect |
| 9. #16811555 | C4 | semidirect |
| 10. D53⋊C32 | C4 | semidirect |
| 16. #16810457 | C4 | semidirect |
| 18. C32×D53 | C4 | semidirect |
| 19. C53×M64 | C4 | semidirect |
| 30. #13133267 | C2×C4 | semidirect |
| 37. #13133123 | C2×C4 | semidirect |
| 39. C32×C53 | C2×C4 | semidirect |
| 96. D53 | #1398 | semidirect |
| 104. M64 | #6157 | semidirect |
| 111. C53 | C2×#1398 | semidirect |
| 131. C32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| C2×#16811510 | 2 |
| #20289825 | 2 |
| #20289824 | 2 |
| M64×D53 | 2 |
| C2×#1398 | 53 |