Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 2. #20292533 | C2 | semidirect |
| 3. #20292525 | C2 | semidirect |
| 4. #20292511 | C2 | semidirect |
| 45. C22×C4×C107 | Q8 | semidirect |
| 103. C107 | #2855 | semidirect |
| 141. C22×C4 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812088 | 2 |
| #20292533 | 2 |
| #20292525 | 2 |
| #20292511 | 2 |
| #20292500 | 2 |
| #20292490 | 2 |
| #20292487 | 2 |
| C22×C42×C107 | 2 |
| #2855 | 107 |