Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 64 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×#16811528 | C2 | semidirect |
| 2. #20289846 | C2 | direct (N × H) |
| 6. #16811528 | C22 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 12. C2×C4×#88322 | C4 | semidirect |
| 13. C2×#127×C53 | C4 | semidirect |
| 29. C4×#88322 | C2×C4 | semidirect |
| 34. #127×C53 | C2×C4 | semidirect |
| 123. C2×C53 | #1408 | semidirect |
| 129. C2×#127 | #6157 | semidirect |
| 137. C53 | C2×#1408 | semidirect |
| 153. #127 | C2×#6157 | semidirect |
| 245. C2 | #20289846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811528 | 2 |
| #20289846 | 2 |
| C2×#16810999 | 2 |
| C2×#1408 | 53 |