Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #16812042 | C4 | semidirect |
| 14. #16812040 | C4 | semidirect |
| 15. #16812020 | C4 | semidirect |
| 73. C107⋊C8 | C42 | semidirect |
| 99. C107 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812042 | 2 |
| C2×#16812040 | 2 |
| C2×#16812020 | 2 |
| C4×C4⋊Dic107 | 2 |
| #20292389 | 2 |
| C4×C4⋊C4×C107 | 2 |
| #1776 | 107 |