Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 7. #16812109 | C4 | semidirect |
| 60. C4×C107 | #103 | semidirect |
| 72. C107 | #1981 | semidirect |
| 134. C4 | #16812034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812109 | 2 |
| C2×#16812034 | 2 |
| C4×C4⋊Dic107 | 2 |
| C2×C4⋊C8×C107 | 2 |
| #1981 | 107 |