Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
556 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 1. C2×#16812101 | C2 | semidirect |
| 2. #20292525 | C2 | semidirect |
| 3. #20292511 | C2 | semidirect |
| 5. #20292493 | C2 | semidirect |
| 74. C22×C107 | #125 | semidirect |
| 93. C107 | #2851 | semidirect |
| 167. C22 | #16812101 | semidirect |
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 |
| #20292500 | 2 |
| #20292493 | 2 |
| #20292487 | 2 |
| C22×C42×C107 | 2 |
| #2851 | 107 |