Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 5. #16811516 | C4 | direct (N × H) |
| 6. #16811511 | C4 | semidirect |
| 7. C4×#11719910 | C4 | semidirect |
| 42. #11719910 | C42 | semidirect |
| 61. C4×C53 | #347 | semidirect |
| 81. C53 | C4×#347 | semidirect |
| 130. C4 | #16811516 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811516 | 2 |
| C4×#13133291 | 2 |
| C4×#13133127 | 2 |
| C4×#347 | 53 |