Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
250 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20272848 | C2 | semidirect |
| 4. C4×#13133123 | C2 | semidirect |
| 5. C4×C32×C53 | C2 | semidirect |
| 9. #16810456 | C4 | direct (N × H) |
| 26. #13133123 | C2×C4 | semidirect |
| 30. C32×C53 | C2×C4 | semidirect |
| 64. C4×C53 | M64 | semidirect |
| 73. C4×C32 | D53 | semidirect |
| 87. C53 | C4×M64 | semidirect |
| 102. C32 | C4×D53 | semidirect |
| 137. C4 | #16810456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810456 | 2 |
| C4×C16×D53 | 2 |
| #20272848 | 2 |
| C4×#13133123 | 2 |
| C4×C32×C53 | 2 |
| C4×M64 | 53 |