Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. #16812019 | C4 | semidirect |
| 63. C8×C107 | C4⋊C4 | semidirect |
| 64. C107⋊C8 | C4⋊C4 | semidirect |
| 85. C107 | #1847 | semidirect |
| 149. C8 | Dic107⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812043 | 2 |
| C2×#16812042 | 2 |
| C2×#16812040 | 2 |
| C2×#16812019 | 2 |
| #20292496 | 2 |
| #20292492 | 2 |
| C2×#106×C107 | 2 |
| #1847 | 107 |