Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 8. #16812101 | C4 | direct (N × H) |
| 68. C4×C107 | #125 | semidirect |
| 77. C107 | C4×#125 | semidirect |
| 147. C4 | #16812101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812101 | 2 |
| #20292525 | 2 |
| #20292511 | 2 |
| #20292493 | 2 |
| C4×Dic107⋊C4 | 2 |
| C4×C4⋊Dic107 | 2 |
| C43×C107 | 2 |
| C4×#125 | 107 |