Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
914 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 251 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×#16811026 | C2 | semidirect |
| 4. #20274387 | C2 | direct (N × H) |
| 5. C2×#16810344 | C2 | semidirect |
| 6. C2×C53×#494 | C2 | semidirect |
| 11. #16811026 | C22 | semidirect |
| 19. #16810344 | C22 | semidirect |
| 23. C53×#494 | C22 | semidirect |
| 125. C2×#494 | D53 | semidirect |
| 130. C2×C53 | #1722 | semidirect |
| 142. #494 | C2×D53 | semidirect |
| 152. C53 | C2×#1722 | semidirect |
| 252. C2 | #20274387 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811026 | 2 |
| C2×#16810996 | 2 |
| C2×#16810971 | 2 |
| #20274387 | 2 |
| C2×#16810344 | 2 |
| C2×C53×#494 | 2 |
| C2×#1722 | 53 |