Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
162 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#13133802 | C4 | semidirect |
| 6. C22×C107⋊C8 | C4 | semidirect |
| 7. #16812028 | C4 | semidirect |
| 74. C107 | #1395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292611 | 2 |
| #20292594 | 2 |
| #410×C107 | 2 |
| #1395 | 107 |